In this paper,we consider the maximal positive definite solution of the nonlinear matrix equation.By using the idea of Algorithm 2.1 in ZHANG(2013),a new inversion-free method with a stepsize parameter is proposed to ...In this paper,we consider the maximal positive definite solution of the nonlinear matrix equation.By using the idea of Algorithm 2.1 in ZHANG(2013),a new inversion-free method with a stepsize parameter is proposed to obtain the maximal positive definite solution of nonlinear matrix equation X+A^(*)X|^(-α)A=Q with the case 0<α≤1.Based on this method,a new iterative algorithm is developed,and its convergence proof is given.Finally,two numerical examples are provided to show the effectiveness of the proposed method.展开更多
This study presents an effective hybrid simulation approach for simulating broadband ground motion in complex near-fault locations.The approach utilizes a deterministic approach based on the spectral element method(SE...This study presents an effective hybrid simulation approach for simulating broadband ground motion in complex near-fault locations.The approach utilizes a deterministic approach based on the spectral element method(SEM),which is used to simulate low-frequency ground motion(f<1 Hz)by incorporating an innovative efficient discontinuous Galerkin(DG)method for grid division to accurately model basin sedimentary layers at reduced costs.It also introduces a comprehensive hybrid source model for high-frequency random scattering and a nonlinear analysis module for basin sedimentary layers.Deterministic outcomes are combined with modified three-dimensional stochastic finite fault method(3D-EXSIM)simulations of high-frequency ground motion(f>1 Hz).A fourth-order Butterworth filter with zero phase shift is employed for time-domain filtering of low-and high-frequency time series at a crossover frequency of 1 Hz,merging the low and high-frequency ground motions into a broadband time series.Taking an Ms 6.8 Luding earthquake,as an example,this hybrid method was used for a rapid and efficient simulation analysis of broadband ground motion in the region.The accuracy and efficiency of this hybrid method were verified through comparisons with actually observed station data and empirical attenuation curves.Deterministic method simulation results revealed the effects of mountainous topography,basin effects,nonlinear effects within the basin’s sedimentary layers,and a coupling interaction between the basin and the mountains.The findings are consistent with similar studies,showing that near-fault sedimentary basins significantly focus and amplify strong ground motion,and the soil’s nonlinear behavior in the basin influences ground motion to varying extents at different distances from the fault.The mountainous topography impacts the basin’s response to ground motion,leading to barrier effects.This research provides a scientific foundation for seismic zoning,urban planning,and seismic design in nearfault mountain basin regions.展开更多
Objectives This review aimed to systematically synthesize the available research on the disclosure of diagnosis and related issues in childhood cancer from the perspectives of healthcare professionals,with the goal of...Objectives This review aimed to systematically synthesize the available research on the disclosure of diagnosis and related issues in childhood cancer from the perspectives of healthcare professionals,with the goal of informing the optimization of disclosure processes and meeting the communication needs of affected families.Methods In accordance with the Joanna Briggs Institute(JBI)methodology for mixed methods systematic reviews,the convergent segregated approach was used in this review.Articles were retrieved from 11 databases,including PubMed,Web of Science,CINAHL,CENTRAL,Embase,Ovid/Medline,PsycINFO,PsycArticles,Scopus,ERIC,and China National Knowledge Infrastructure(CNKI).The quality of the selected articles was assessed using the Mixed Method Appraisal Tool(MMAT).The review protocol was registered on PROSPERO(CRD42024542746).Results A total of 21 studies from 10 countries were included.Their methodological quality was generally medium to high,with MMAT scores ranging from 60%to 100%.The synthesis yielded three core themes:1)the spectrum of professional and societal attitudes toward disclosure;2)the dynamic practices of navigating disclosure amid uncertainty,including timing and environment,stakeholders,and content of disclosure;and 3)factors influencing disclosure,including children’s,parental,healthcare professionals’,and socio-cultural factors.Conclusions This review synthesized the perspectives and experiences of healthcare professionals regarding disclosure in childhood cancer,highlighting the complexity and multidimensional nature of this process in clinical practice.Future research should further investigate the experiences and needs of children and their parents,explore cultural variations in disclosure practices,develop context-appropriate assessment tools,and construct multidimensional intervention strategies to enhance the humanistic care and professional effectiveness of the disclosure process.展开更多
In this paper,a novel method for investigating the particle-crushing behavior of breeding particles in a fusion blanket is proposed.The fractal theory and Weibull distribution are combined to establish a theoretical m...In this paper,a novel method for investigating the particle-crushing behavior of breeding particles in a fusion blanket is proposed.The fractal theory and Weibull distribution are combined to establish a theoretical model,and its validity was verified using a simple impact test.A crushable discrete element method(DEM)framework is built based on the previously established theoretical model.The tensile strength,which considers the fractal theory,size effect,and Weibull variation,was assigned to each generated particle.The assigned strength is then used for crush detection by comparing it with its maximum tensile stress.Mass conservation is ensured by inserting a series of sub-particles whose total mass was equal to the quality loss.Based on the crushable DEM framework,a numerical simulation of the crushing behavior of a pebble bed with hollow cylindrical geometry under a uniaxial compression test was performed.The results of this investigation showed that the particle withstands the external load by contact and sliding at the beginning of the compression process,and the results confirmed that crushing can be considered an important method of resisting the increasing external load.A relatively regular particle arrangement aids in resisting the load and reduces the occurrence of particle crushing.However,a limit exists to the promotion of resistance.When the strain increases beyond this limit,the distribution of the crushing position tends to be isotropic over the entire pebble bed.The theoretical model and crushable DEM framework provide a new method for exploring the pebble bed in a fusion reactor,considering particle crushing.展开更多
A new quadrilateral edge element method is proposed and analyzed for Maxwell equations.This proposed method is based on Duan-Liang quadrilateral element(Math.Comp.73(2004),pp.1–18).When applied to the eigenvalue prob...A new quadrilateral edge element method is proposed and analyzed for Maxwell equations.This proposed method is based on Duan-Liang quadrilateral element(Math.Comp.73(2004),pp.1–18).When applied to the eigenvalue problem,the method is spectral-correct and spurious-free.Stability and error estimates are obtained,including the interpolation error estimates and the error estimates between the finite element solution and the exact solution.The method is suitable for singular solution as well as smooth solution,and consequently,the method is valid for nonconvex domains which may have a number of reentrant corners.Of course,the method is suitable for arbitrary quadrilaterals(under the usual shape-regular condition).展开更多
Effective partitioning is crucial for enabling parallel restoration of power systems after blackouts.This paper proposes a novel partitioning method based on deep reinforcement learning.First,the partitioning decision...Effective partitioning is crucial for enabling parallel restoration of power systems after blackouts.This paper proposes a novel partitioning method based on deep reinforcement learning.First,the partitioning decision process is formulated as a Markov decision process(MDP)model to maximize the modularity.Corresponding key partitioning constraints on parallel restoration are considered.Second,based on the partitioning objective and constraints,the reward function of the partitioning MDP model is set by adopting a relative deviation normalization scheme to reduce mutual interference between the reward and penalty in the reward function.The soft bonus scaling mechanism is introduced to mitigate overestimation caused by abrupt jumps in the reward.Then,the deep Q network method is applied to solve the partitioning MDP model and generate partitioning schemes.Two experience replay buffers are employed to speed up the training process of the method.Finally,case studies on the IEEE 39-bus test system demonstrate that the proposed method can generate a high-modularity partitioning result that meets all key partitioning constraints,thereby improving the parallelism and reliability of the restoration process.Moreover,simulation results demonstrate that an appropriate discount factor is crucial for ensuring both the convergence speed and the stability of the partitioning training.展开更多
The application of nitrogen fertilizers in agricultural fields can lead to the release of nitrogen-containing gases(NCGs),such as NO_(x),NH_(3) and N_(2)O,which can significantly impact regional atmospheric environmen...The application of nitrogen fertilizers in agricultural fields can lead to the release of nitrogen-containing gases(NCGs),such as NO_(x),NH_(3) and N_(2)O,which can significantly impact regional atmospheric environment and con-tribute to global climate change.However,there remain considerable research gaps in the accurate measurement of NCGs emissions from agricultural fields,hindering the development of effective emission reduction strategies.We improved an open-top dynamic chambers(OTDCs)system and evaluated the performance by comparing the measured and given fluxes of the NCGs.The results showed that the measured fluxes of NO,N_(2)O and NH_(3)were 1%,2%and 7%lower than the given fluxes,respectively.For the determination of NH_(3) concentration,we employed a stripping coil-ion chromatograph(SC-IC)analytical technique,which demonstrated an absorption efficiency for atmospheric NH_(3) exceeding 96.1%across sampling durations of 6 to 60 min.In the summer maize season,we utilized the OTDCs system to measure the exchange fluxes of NO,NH_(3),and N_(2)O from the soil in the North China Plain.Substantial emissions of NO,NH_(3) and N_(2)O were recorded following fertilization,with peaks of 107,309,1239 ng N/(m^(2)·s),respectively.Notably,significant NCGs emissions were observed following sus-tained heavy rainfall one month after fertilization,particularly with NH_(3) peak being 4.5 times higher than that observed immediately after fertilization.Our results demonstrate that the OTDCs system accurately reflects the emission characteristics of soil NCGs and meets the requirements for long-term and continuous flux observation.展开更多
Convex feasibility problems are widely used in image reconstruction, sparse signal recovery, and other areas. This paper is devoted to considering a class of convex feasibility problem arising from sparse signal recov...Convex feasibility problems are widely used in image reconstruction, sparse signal recovery, and other areas. This paper is devoted to considering a class of convex feasibility problem arising from sparse signal recovery. We first derive the projection formulas for a vector onto the feasible sets. The centralized circumcentered-reflection method is designed to solve the convex feasibility problem. Some numerical experiments demonstrate the feasibility and effectiveness of the proposed algorithm, showing superior performance compared to conventional alternating projection methods.展开更多
Marine thin plates are susceptible to welding deformation owing to their low structural stiffness.Therefore,the efficient and accurate prediction of welding deformation is essential for improving welding quality.The t...Marine thin plates are susceptible to welding deformation owing to their low structural stiffness.Therefore,the efficient and accurate prediction of welding deformation is essential for improving welding quality.The traditional thermal elastic-plastic finite element method(TEP-FEM)can accurately predict welding deformation.However,its efficiency is low because of the complex nonlinear transient computation,making it difficult to meet the needs of rapid engineering evaluation.To address this challenge,this study proposes an efficient prediction method for welding deformation in marine thin plate butt welds.This method is based on the coupled temperature gradient-thermal strain method(TG-TSM)that integrates inherent strain theory with a shell element finite element model.The proposed method first extracts the distribution pattern and characteristic value of welding-induced inherent strain through TEP-FEM analysis.This strain is then converted into the equivalent thermal load applied to the shell element model for rapid computation.The proposed method-particularly,the gradual temperature gradient-thermal strain method(GTG-TSM)-achieved improved computational efficiency and consistent precision.Furthermore,the proposed method required much less computation time than the traditional TEP-FEM.Thus,this study lays the foundation for future prediction of welding deformation in more complex marine thin plates.展开更多
Advanced intensity measures(IMs)based on an inelastic deformation spectrum improved the evaluation of the median engineering demand parameters(EDPs)and reduced dispersion.In this regard,an optimized two-degreefreedom(...Advanced intensity measures(IMs)based on an inelastic deformation spectrum improved the evaluation of the median engineering demand parameters(EDPs)and reduced dispersion.In this regard,an optimized two-degreefreedom(2DOF)modal pushover-based scaling procedure(2DMPS)has been developed for a nonlinear dynamic analysis of asymmetric in-plan buildings.The 2DMPS procedure scales ground motions to approach close enough to a target value of the inelastic displacement of the first-mode inelastic 2DOF modal stick,extended for structures with significant contributions of higher modes.Further,4-,6-and 13-story RC SMRF buildings were selected for analyses using ground motion records scaled by the 2DMPS procedure,the modal pushover-based scaling method(MPS),and ASCE/SEI 7-16 scaling procedures.The median values of EDPs on scaled records closely matched the benchmark results.The bias in the EDP values due to the scaled records in every group regarding their median value was lower than the dispersion of the 21 unscaled records.These results generally demonstrate the accuracy and efficiency of the 2DMPS method.Additionally,the 2DOF modal stick’s inelastic response spectra are better suited for calculating seismic demands for one-way asymmetric-plan structures than the SDOF inelastic response spectra.展开更多
At present,there is currently a lack of unified standard methods for the determination of antimony content in groundwater in China.The precision and trueness of related detection technologies have not yet been systema...At present,there is currently a lack of unified standard methods for the determination of antimony content in groundwater in China.The precision and trueness of related detection technologies have not yet been systematically and quantitatively evaluated,which limits the effective implementation of environmental monitoring.In response to this key technical gap,this study aimed to establish a standardized method for determining antimony in groundwater using Hydride Generation–Atomic Fluorescence Spectrometry(HG-AFS).Ten laboratories participated in inter-laboratory collaborative tests,and the statistical analysis of the test data was carried out in strict accordance with the technical specifications of GB/T 6379.2—2004 and GB/T 6379.4—2006.The consistency and outliers of the data were tested by Mandel's h and k statistics,the Grubbs test and the Cochran test,and the outliers were removed to optimize the data,thereby significantly improving the reliability and accuracy.Based on the optimized data,parameters such as the repeatability limit(r),reproducibility limit(R),and method bias value(δ)were determined,and the trueness of the method was statistically evaluated.At the same time,precision-function relationships were established,and all results met the requirements.The results show that the lower the antimony content,the lower the repeatability limit(r)and reproducibility limit(R),indicating that the measurement error mainly originates from the detection limit of the method and instrument sensitivity.Therefore,improving the instrument sensitivity and reducing the detection limit are the keys to controlling the analytical error and improving precision.This study provides reliable data support and a solid technical foundation for the establishment and evaluation of standardized methods for the determination of antimony content in groundwater.展开更多
The stochastic extended finite-fault simulation method(EXSIM)is a widely used tool in seismological research,with applications in ground motion prediction and simulation,seismic hazard analysis,and engineering studies...The stochastic extended finite-fault simulation method(EXSIM)is a widely used tool in seismological research,with applications in ground motion prediction and simulation,seismic hazard analysis,and engineering studies.However,recent studies have revealed a significant limitation:EXSIM tends to overpredict ground motions in the low-to-intermediate frequency range,particularly for large thrust earthquakes that are often characterized by a double-corner-frequency source model.To address this issue and enhance simulation accuracy,this study introduces two key improvements:(1)a novel asperity-distributed stress-drop composite fault model and(2)a hybrid application of EXSIM with the composite fault model.The proposed method is validated through its application to the 2013 M_(w)6.7 Lushan earthquake that occurred in China and six thrust earthquakes with an M_(w)≥6.5 in Japan.By comparing the simulated ground motions with recorded data,the results demonstrate that the improved method achieves consistent accuracy across the high-and low-frequency spectrum(combined goodness-of-fit:CGOF<0.35).This study significantly broadens the applicability of stochastic finite-fault simulations,enabling more reliable predictions for a wider range of seismic scenarios,including complex thrust faulting events.展开更多
Stand age plays a crucial role in forest biomass estimation and carbon cycle modeling.Assessing the uncertainty of stand age prediction models and identifying the key driving factors in the modeling process have becom...Stand age plays a crucial role in forest biomass estimation and carbon cycle modeling.Assessing the uncertainty of stand age prediction models and identifying the key driving factors in the modeling process have become major challenges in forestry research.In this study,we selected the Shaanxi-Gansu-Ningxia region of Northeast China as the research area and utilized multi-source datasets from the summer of 2019 to extract information on spectral,textural,climatic,water balance,and stand characteristics.By integrating the Random Forest(RF)model with Monte Carlo(MC)simulation,we constructed six regression models based on different combina-tions of features and evaluated the uncertainty of each model.Furthermore,we investigated the driving factors influencing stand age modeling by analyzing the effects of different types of features on age inversion.Model performance and accuracy were assessed using the root mean square error(RMSE),mean absolute error(MAE),and the coefficient of determination(R^(2)),while the relative root mean square error(rRMSE)was employed to quantify model uncertainty.The results indicate that the scenarios with more obvious improve-ment in accuracy and effective reduction in uncertainty were Scenario 3 with the inclusion of climate and water balance information(RMSE=25.54 yr,MAE=18.03 yr,R^(2)=0.51,rRMSE=19.17%)and Scenario 5 with the inclusion of stand characterization informa-tion(RMSE=18.47 yr,MAE=13.05 yr,R^(2)=0.74,rRMSE=16.99%).Scenario 6,incorporating all feature types,achieved the highest accuracy(RMSE=17.60 yr,MAE=12.06 yr,R^(2)=0.77,rRMSE=14.19%).In this study,elevation,minimum temperature,and diameter at breast height(DBH)emerged as the key drivers of stand-age modeling.The proposed method can be used to identify drivers and to quantify uncertainty in stand-age estimation,providing a useful reference for improving model accuracy and uncertainty assessment.展开更多
In general, the seismic response analysis in earthquake engineering assumes that the vibration parameters of the target and the contact surface of the external media are identical,i. e., single point input. However, e...In general, the seismic response analysis in earthquake engineering assumes that the vibration parameters of the target and the contact surface of the external media are identical,i. e., single point input. However, earthquake energy has an attenuation phenomenon in wave propagation,so a wide range of soil slopes and the external medium contact surface of different input points on motion are not identical. If we consider single point input only, it may not correspond with reality, so it is necessary to carry out research on multi-point input methods. Based on the 2-D slope model,single-point input and multi-point input are performed respectively to analyze and compare their similarities and differences in the perspectives of the characteristics of seismic response of soil layer and plastic zone distribution to provide a reference for the seismic design of slopes. The results show that in the perspective of soil seismic response analysis,the peak acceleration output and peak velocity output under multi-point input are greater than the peak values under single point input at the same monitoring point,the peak appearing time is also earlier than that of the single point input; in terms of the plastic zone distribution,the multi-point effect is manifested as the presence of more obvious tensile shear failures; in the perspective of safety coefficient,the safety coefficient under each multi-point input is smaller than that of single point input,a difference of about 7 % or so. In summary,multi-point input is more reasonable and practical than single point input,so multi-point input should be considered in seismic design.展开更多
Purpose – Straightness measurement of rail weld joint is of essential importance to railway maintenance. Dueto the lack of efficient measurement equipment, there has been limited in-depth research on rail weld joint ...Purpose – Straightness measurement of rail weld joint is of essential importance to railway maintenance. Dueto the lack of efficient measurement equipment, there has been limited in-depth research on rail weld joint with a5-m wavelength range, leaving a significant knowledge gap in this field.Design/methodology/approach – In this study, the authors used the well-established inertial referencemethod (IR-method), and the state-of-the-art multi-point chord reference method (MCR-method). Two methodshave been applied in different types of rail straightness measurement trollies, respectively. These instrumentswere tested in a high-speed rail section within a certain region of China. The test results were ultimatelyvalidated through using traditional straightedge and feeler gauge methods as reference data to evaluate the railweld joint straightness within the 5-m wavelength range.Findings – The research reveals that IR-method and MCR-method produce reasonably similar measurementresults for wavelengths below 1 m. However, MCR-method outperforms IR-method in terms of accuracy forwavelengths exceeding 3 m. Furthermore, it was observed that IR-method, while operating at a slower speed,carries the risk of derailing and is incapable of detecting rail weld joints and low joints within the track.Originality/value – The research compare two methods’ measurement effects in a longer wavelength rangeand demonstrate the superiority of MCR-method.展开更多
The centroid coordinate serves as a critical control parameter in motion systems,including aircraft,missiles,rockets,and drones,directly influencing their motion dynamics and control performance.Traditional methods fo...The centroid coordinate serves as a critical control parameter in motion systems,including aircraft,missiles,rockets,and drones,directly influencing their motion dynamics and control performance.Traditional methods for centroid measurement often necessitate custom equipment and specialized positioning devices,leading to high costs and limited accuracy.Here,we present a centroid measurement method that integrates 3D scanning technology,enabling accurate measurement of centroid across various types of objects without the need for specialized positioning fixtures.A theoretical framework for centroid measurement was established,which combined the principle of the multi-point weighing method with 3D scanning technology.The measurement accuracy was evaluated using a designed standard component.Experimental results demonstrate that the discrepancies between the theoretical and the measured centroid of a standard component with various materials and complex shapes in the X,Y,and Z directions are 0.003 mm,0.009 mm,and 0.105 mm,respectively,yielding a spatial deviation of 0.106 mm.Qualitative verification was conducted through experimental validation of three distinct types.They confirmed the reliability of the proposed method,which allowed for accurate centroid measurements of various products without requiring positioning fixtures.This advancement significantly broadened the applicability and scope of centroid measurement devices,offering new theoretical insights and methodologies for the measurement of complex parts and systems.展开更多
Fast and accurate identification of unknown pollution sources plays a crucial role in the emergency response and source control of air pollution.In this work,the applicability of a previously proposed two-step inversi...Fast and accurate identification of unknown pollution sources plays a crucial role in the emergency response and source control of air pollution.In this work,the applicability of a previously proposed two-step inversion method is investigated with sensitivity experiments and real data from the first release of the European Tracer Experiment(ETEX-1).The two-step inversion method is based on the principle of least squares and carries out additional model correction through the residual iterative process.To evaluate its performance,its retrieval results are compared with those of two other existing algorithms.It is shown that for those cases with richer measurements,all three methods are less sensitive to errors,while for cases where measurements are sparse,their retrieval accuracy will rapidly decrease as errors increase.From the results of sensitivity experiments,the new method provides higher estimation accuracy and a more stable performance than the other two methods.The new method presents the smallest maximum location error of 18.20 km when the amplitude of the measurement error increases to 100%,and 22.67 km when errors in the wind fields increase to 200%.Moreover,when applied to ETEX-1 data,the new method also exhibits good performance,with a location error of 4.71 km,which is the best estimation with respect to source location.展开更多
Modal parameters can accurately characterize the structural dynamic properties and assess the physical state of the structure.Therefore,it is particularly significant to identify the structural modal parameters accordi...Modal parameters can accurately characterize the structural dynamic properties and assess the physical state of the structure.Therefore,it is particularly significant to identify the structural modal parameters according to the monitoring data information in the structural health monitoring(SHM)system,so as to provide a scientific basis for structural damage identification and dynamic model modification.In view of this,this paper reviews methods for identifying structural modal parameters under environmental excitation and briefly describes how to identify structural damages based on the derived modal parameters.The paper primarily introduces data-driven modal parameter recognition methods(e.g.,time-domain,frequency-domain,and time-frequency-domain methods,etc.),briefly describes damage identification methods based on the variations of modal parameters(e.g.,natural frequency,modal shapes,and curvature modal shapes,etc.)and modal validation methods(e.g.,Stability Diagram and Modal Assurance Criterion,etc.).The current status of the application of artificial intelligence(AI)methods in the direction of modal parameter recognition and damage identification is further discussed.Based on the pre-vious analysis,the main development trends of structural modal parameter recognition and damage identification methods are given to provide scientific references for the optimized design and functional upgrading of SHM systems.展开更多
To analyze the differences in the transport and distribution of different types of proppants and to address issues such as the short effective support of proppant and poor placement in hydraulically intersecting fract...To analyze the differences in the transport and distribution of different types of proppants and to address issues such as the short effective support of proppant and poor placement in hydraulically intersecting fractures,this study considered the combined impact of geological-engineering factors on conductivity.Using reservoir production parameters and the discrete elementmethod,multispherical proppants were constructed.Additionally,a 3D fracture model,based on the specified conditions of the L block,employed coupled(Computational Fluid Dynamics)CFD-DEM(Discrete ElementMethod)for joint simulations to quantitatively analyze the transport and placement patterns of multispherical proppants in intersecting fractures.Results indicate that turbulent kinetic energy is an intrinsic factor affecting proppant transport.Moreover,the efficiency of placement and migration distance of low-sphericity quartz sand constructed by the DEM in the main fracture are significantly reduced compared to spherical ceramic proppants,with a 27.7%decrease in the volume fraction of the fracture surface,subsequently affecting the placement concentration and damaging fracture conductivity.Compared to small-angle fractures,controlling artificial and natural fractures to expand at angles of 45°to 60°increases the effective support length by approximately 20.6%.During hydraulic fracturing of gas wells,ensuring the fracture support area and post-closure conductivity can be achieved by controlling the sphericity of proppants and adjusting the perforation direction to control the direction of artificial fractures.展开更多
We consider a uniform finite difference method for nonlinear singularly perturbed multi-point boundary value problem on Shishkin mesh. The problem is discretized using integral identities, interpolating quadrature rul...We consider a uniform finite difference method for nonlinear singularly perturbed multi-point boundary value problem on Shishkin mesh. The problem is discretized using integral identities, interpolating quadrature rules, exponential basis functions and remainder terms in integral form. We show that this method is the first order convergent in the discrete maximum norm for original problem (independent of the perturbation parameter ε). To illustrate the theoretical results, we solve test problem and we also give the error distributions in the solution in Table 1 and Figures 1-3.展开更多
基金Supported in part by Natural Science Foundation of Guangxi(2023GXNSFAA026246)in part by the Central Government's Guide to Local Science and Technology Development Fund(GuikeZY23055044)in part by the National Natural Science Foundation of China(62363003)。
文摘In this paper,we consider the maximal positive definite solution of the nonlinear matrix equation.By using the idea of Algorithm 2.1 in ZHANG(2013),a new inversion-free method with a stepsize parameter is proposed to obtain the maximal positive definite solution of nonlinear matrix equation X+A^(*)X|^(-α)A=Q with the case 0<α≤1.Based on this method,a new iterative algorithm is developed,and its convergence proof is given.Finally,two numerical examples are provided to show the effectiveness of the proposed method.
基金National Natural Science Foundation of China under Grant Nos.U2139208 and 52278516Key Laboratory of Earthquake Engineering and Engineering Vibration,China Earthquake Administration under Grant No.2024D15Key Laboratory of Soft Soil Characteristic and Engineering Environment,Tianjin Chengjian University under Grant No.2022SCEEKL003。
文摘This study presents an effective hybrid simulation approach for simulating broadband ground motion in complex near-fault locations.The approach utilizes a deterministic approach based on the spectral element method(SEM),which is used to simulate low-frequency ground motion(f<1 Hz)by incorporating an innovative efficient discontinuous Galerkin(DG)method for grid division to accurately model basin sedimentary layers at reduced costs.It also introduces a comprehensive hybrid source model for high-frequency random scattering and a nonlinear analysis module for basin sedimentary layers.Deterministic outcomes are combined with modified three-dimensional stochastic finite fault method(3D-EXSIM)simulations of high-frequency ground motion(f>1 Hz).A fourth-order Butterworth filter with zero phase shift is employed for time-domain filtering of low-and high-frequency time series at a crossover frequency of 1 Hz,merging the low and high-frequency ground motions into a broadband time series.Taking an Ms 6.8 Luding earthquake,as an example,this hybrid method was used for a rapid and efficient simulation analysis of broadband ground motion in the region.The accuracy and efficiency of this hybrid method were verified through comparisons with actually observed station data and empirical attenuation curves.Deterministic method simulation results revealed the effects of mountainous topography,basin effects,nonlinear effects within the basin’s sedimentary layers,and a coupling interaction between the basin and the mountains.The findings are consistent with similar studies,showing that near-fault sedimentary basins significantly focus and amplify strong ground motion,and the soil’s nonlinear behavior in the basin influences ground motion to varying extents at different distances from the fault.The mountainous topography impacts the basin’s response to ground motion,leading to barrier effects.This research provides a scientific foundation for seismic zoning,urban planning,and seismic design in nearfault mountain basin regions.
基金supported by the Fuxing Nursing Research Foundation of Fudan University[FNF202352].
文摘Objectives This review aimed to systematically synthesize the available research on the disclosure of diagnosis and related issues in childhood cancer from the perspectives of healthcare professionals,with the goal of informing the optimization of disclosure processes and meeting the communication needs of affected families.Methods In accordance with the Joanna Briggs Institute(JBI)methodology for mixed methods systematic reviews,the convergent segregated approach was used in this review.Articles were retrieved from 11 databases,including PubMed,Web of Science,CINAHL,CENTRAL,Embase,Ovid/Medline,PsycINFO,PsycArticles,Scopus,ERIC,and China National Knowledge Infrastructure(CNKI).The quality of the selected articles was assessed using the Mixed Method Appraisal Tool(MMAT).The review protocol was registered on PROSPERO(CRD42024542746).Results A total of 21 studies from 10 countries were included.Their methodological quality was generally medium to high,with MMAT scores ranging from 60%to 100%.The synthesis yielded three core themes:1)the spectrum of professional and societal attitudes toward disclosure;2)the dynamic practices of navigating disclosure amid uncertainty,including timing and environment,stakeholders,and content of disclosure;and 3)factors influencing disclosure,including children’s,parental,healthcare professionals’,and socio-cultural factors.Conclusions This review synthesized the perspectives and experiences of healthcare professionals regarding disclosure in childhood cancer,highlighting the complexity and multidimensional nature of this process in clinical practice.Future research should further investigate the experiences and needs of children and their parents,explore cultural variations in disclosure practices,develop context-appropriate assessment tools,and construct multidimensional intervention strategies to enhance the humanistic care and professional effectiveness of the disclosure process.
基金supported by Anhui Provincial Natural Science Foundation(2408085QA030)Natural Science Research Project of Anhui Educational Committee,China(2022AH050825)+3 种基金Medical Special Cultivation Project of Anhui University of Science and Technology(YZ2023H2C008)the Excellent Research and Innovation Team of Anhui Province,China(2022AH010052)the Scientific Research Foundation for High-level Talents of Anhui University of Science and Technology,China(2021yjrc51)Collaborative Innovation Program of Hefei Science Center,CAS,China(2019HSC-CIP006).
文摘In this paper,a novel method for investigating the particle-crushing behavior of breeding particles in a fusion blanket is proposed.The fractal theory and Weibull distribution are combined to establish a theoretical model,and its validity was verified using a simple impact test.A crushable discrete element method(DEM)framework is built based on the previously established theoretical model.The tensile strength,which considers the fractal theory,size effect,and Weibull variation,was assigned to each generated particle.The assigned strength is then used for crush detection by comparing it with its maximum tensile stress.Mass conservation is ensured by inserting a series of sub-particles whose total mass was equal to the quality loss.Based on the crushable DEM framework,a numerical simulation of the crushing behavior of a pebble bed with hollow cylindrical geometry under a uniaxial compression test was performed.The results of this investigation showed that the particle withstands the external load by contact and sliding at the beginning of the compression process,and the results confirmed that crushing can be considered an important method of resisting the increasing external load.A relatively regular particle arrangement aids in resisting the load and reduces the occurrence of particle crushing.However,a limit exists to the promotion of resistance.When the strain increases beyond this limit,the distribution of the crushing position tends to be isotropic over the entire pebble bed.The theoretical model and crushable DEM framework provide a new method for exploring the pebble bed in a fusion reactor,considering particle crushing.
基金supported by the National Natural Science Foundation of China(12401482)the second author was supported by the National Natural Science Foundation of China(12371371,12261160361,11971366)supported by the Open Research Fund of Hubei Key Laboratory of Computational Science,Wuhan University.
文摘A new quadrilateral edge element method is proposed and analyzed for Maxwell equations.This proposed method is based on Duan-Liang quadrilateral element(Math.Comp.73(2004),pp.1–18).When applied to the eigenvalue problem,the method is spectral-correct and spurious-free.Stability and error estimates are obtained,including the interpolation error estimates and the error estimates between the finite element solution and the exact solution.The method is suitable for singular solution as well as smooth solution,and consequently,the method is valid for nonconvex domains which may have a number of reentrant corners.Of course,the method is suitable for arbitrary quadrilaterals(under the usual shape-regular condition).
基金funded by the Beijing Engineering Research Center of Electric Rail Transportation.
文摘Effective partitioning is crucial for enabling parallel restoration of power systems after blackouts.This paper proposes a novel partitioning method based on deep reinforcement learning.First,the partitioning decision process is formulated as a Markov decision process(MDP)model to maximize the modularity.Corresponding key partitioning constraints on parallel restoration are considered.Second,based on the partitioning objective and constraints,the reward function of the partitioning MDP model is set by adopting a relative deviation normalization scheme to reduce mutual interference between the reward and penalty in the reward function.The soft bonus scaling mechanism is introduced to mitigate overestimation caused by abrupt jumps in the reward.Then,the deep Q network method is applied to solve the partitioning MDP model and generate partitioning schemes.Two experience replay buffers are employed to speed up the training process of the method.Finally,case studies on the IEEE 39-bus test system demonstrate that the proposed method can generate a high-modularity partitioning result that meets all key partitioning constraints,thereby improving the parallelism and reliability of the restoration process.Moreover,simulation results demonstrate that an appropriate discount factor is crucial for ensuring both the convergence speed and the stability of the partitioning training.
基金supported by the National Key Research and Develop-ment Program(No.2022YFC3701103)the National Natural Science Foundation of China(Nos.42130714 and 41931287).
文摘The application of nitrogen fertilizers in agricultural fields can lead to the release of nitrogen-containing gases(NCGs),such as NO_(x),NH_(3) and N_(2)O,which can significantly impact regional atmospheric environment and con-tribute to global climate change.However,there remain considerable research gaps in the accurate measurement of NCGs emissions from agricultural fields,hindering the development of effective emission reduction strategies.We improved an open-top dynamic chambers(OTDCs)system and evaluated the performance by comparing the measured and given fluxes of the NCGs.The results showed that the measured fluxes of NO,N_(2)O and NH_(3)were 1%,2%and 7%lower than the given fluxes,respectively.For the determination of NH_(3) concentration,we employed a stripping coil-ion chromatograph(SC-IC)analytical technique,which demonstrated an absorption efficiency for atmospheric NH_(3) exceeding 96.1%across sampling durations of 6 to 60 min.In the summer maize season,we utilized the OTDCs system to measure the exchange fluxes of NO,NH_(3),and N_(2)O from the soil in the North China Plain.Substantial emissions of NO,NH_(3) and N_(2)O were recorded following fertilization,with peaks of 107,309,1239 ng N/(m^(2)·s),respectively.Notably,significant NCGs emissions were observed following sus-tained heavy rainfall one month after fertilization,particularly with NH_(3) peak being 4.5 times higher than that observed immediately after fertilization.Our results demonstrate that the OTDCs system accurately reflects the emission characteristics of soil NCGs and meets the requirements for long-term and continuous flux observation.
基金Supported by the Natural Science Foundation of Guangxi Province(Grant Nos.2023GXNSFAA026067,2024GXN SFAA010521)the National Natural Science Foundation of China(Nos.12361079,12201149,12261026).
文摘Convex feasibility problems are widely used in image reconstruction, sparse signal recovery, and other areas. This paper is devoted to considering a class of convex feasibility problem arising from sparse signal recovery. We first derive the projection formulas for a vector onto the feasible sets. The centralized circumcentered-reflection method is designed to solve the convex feasibility problem. Some numerical experiments demonstrate the feasibility and effectiveness of the proposed algorithm, showing superior performance compared to conventional alternating projection methods.
基金Supported by the National Natural Science Foundation of China under Grant No.51975138the High-Tech Ship Scientific Research Project from the Ministry of Industry and Information Technology under Grant No.CJ05N20the National Defense Basic Research Project under Grant No.JCKY2023604C006.
文摘Marine thin plates are susceptible to welding deformation owing to their low structural stiffness.Therefore,the efficient and accurate prediction of welding deformation is essential for improving welding quality.The traditional thermal elastic-plastic finite element method(TEP-FEM)can accurately predict welding deformation.However,its efficiency is low because of the complex nonlinear transient computation,making it difficult to meet the needs of rapid engineering evaluation.To address this challenge,this study proposes an efficient prediction method for welding deformation in marine thin plate butt welds.This method is based on the coupled temperature gradient-thermal strain method(TG-TSM)that integrates inherent strain theory with a shell element finite element model.The proposed method first extracts the distribution pattern and characteristic value of welding-induced inherent strain through TEP-FEM analysis.This strain is then converted into the equivalent thermal load applied to the shell element model for rapid computation.The proposed method-particularly,the gradual temperature gradient-thermal strain method(GTG-TSM)-achieved improved computational efficiency and consistent precision.Furthermore,the proposed method required much less computation time than the traditional TEP-FEM.Thus,this study lays the foundation for future prediction of welding deformation in more complex marine thin plates.
文摘Advanced intensity measures(IMs)based on an inelastic deformation spectrum improved the evaluation of the median engineering demand parameters(EDPs)and reduced dispersion.In this regard,an optimized two-degreefreedom(2DOF)modal pushover-based scaling procedure(2DMPS)has been developed for a nonlinear dynamic analysis of asymmetric in-plan buildings.The 2DMPS procedure scales ground motions to approach close enough to a target value of the inelastic displacement of the first-mode inelastic 2DOF modal stick,extended for structures with significant contributions of higher modes.Further,4-,6-and 13-story RC SMRF buildings were selected for analyses using ground motion records scaled by the 2DMPS procedure,the modal pushover-based scaling method(MPS),and ASCE/SEI 7-16 scaling procedures.The median values of EDPs on scaled records closely matched the benchmark results.The bias in the EDP values due to the scaled records in every group regarding their median value was lower than the dispersion of the 21 unscaled records.These results generally demonstrate the accuracy and efficiency of the 2DMPS method.Additionally,the 2DOF modal stick’s inelastic response spectra are better suited for calculating seismic demands for one-way asymmetric-plan structures than the SDOF inelastic response spectra.
基金supported by the National Natural Science Foundation of China(Project No.42307555).
文摘At present,there is currently a lack of unified standard methods for the determination of antimony content in groundwater in China.The precision and trueness of related detection technologies have not yet been systematically and quantitatively evaluated,which limits the effective implementation of environmental monitoring.In response to this key technical gap,this study aimed to establish a standardized method for determining antimony in groundwater using Hydride Generation–Atomic Fluorescence Spectrometry(HG-AFS).Ten laboratories participated in inter-laboratory collaborative tests,and the statistical analysis of the test data was carried out in strict accordance with the technical specifications of GB/T 6379.2—2004 and GB/T 6379.4—2006.The consistency and outliers of the data were tested by Mandel's h and k statistics,the Grubbs test and the Cochran test,and the outliers were removed to optimize the data,thereby significantly improving the reliability and accuracy.Based on the optimized data,parameters such as the repeatability limit(r),reproducibility limit(R),and method bias value(δ)were determined,and the trueness of the method was statistically evaluated.At the same time,precision-function relationships were established,and all results met the requirements.The results show that the lower the antimony content,the lower the repeatability limit(r)and reproducibility limit(R),indicating that the measurement error mainly originates from the detection limit of the method and instrument sensitivity.Therefore,improving the instrument sensitivity and reducing the detection limit are the keys to controlling the analytical error and improving precision.This study provides reliable data support and a solid technical foundation for the establishment and evaluation of standardized methods for the determination of antimony content in groundwater.
基金National Key Research and Development Program of China under Grant No.2022YFC3003601National Natural Science Foundation of China under Grant No.52478570+1 种基金Heilongjiang Provincial Natural Science Foundation Outstanding Youth Program under Grant No.J020245002the Key Research and Development Program of Xinjiang Production and Construction Corps under Grant No.2024AB077。
文摘The stochastic extended finite-fault simulation method(EXSIM)is a widely used tool in seismological research,with applications in ground motion prediction and simulation,seismic hazard analysis,and engineering studies.However,recent studies have revealed a significant limitation:EXSIM tends to overpredict ground motions in the low-to-intermediate frequency range,particularly for large thrust earthquakes that are often characterized by a double-corner-frequency source model.To address this issue and enhance simulation accuracy,this study introduces two key improvements:(1)a novel asperity-distributed stress-drop composite fault model and(2)a hybrid application of EXSIM with the composite fault model.The proposed method is validated through its application to the 2013 M_(w)6.7 Lushan earthquake that occurred in China and six thrust earthquakes with an M_(w)≥6.5 in Japan.By comparing the simulated ground motions with recorded data,the results demonstrate that the improved method achieves consistent accuracy across the high-and low-frequency spectrum(combined goodness-of-fit:CGOF<0.35).This study significantly broadens the applicability of stochastic finite-fault simulations,enabling more reliable predictions for a wider range of seismic scenarios,including complex thrust faulting events.
基金Under the auspices of the Natural Science Foundation of China(No.32371875,32001249)。
文摘Stand age plays a crucial role in forest biomass estimation and carbon cycle modeling.Assessing the uncertainty of stand age prediction models and identifying the key driving factors in the modeling process have become major challenges in forestry research.In this study,we selected the Shaanxi-Gansu-Ningxia region of Northeast China as the research area and utilized multi-source datasets from the summer of 2019 to extract information on spectral,textural,climatic,water balance,and stand characteristics.By integrating the Random Forest(RF)model with Monte Carlo(MC)simulation,we constructed six regression models based on different combina-tions of features and evaluated the uncertainty of each model.Furthermore,we investigated the driving factors influencing stand age modeling by analyzing the effects of different types of features on age inversion.Model performance and accuracy were assessed using the root mean square error(RMSE),mean absolute error(MAE),and the coefficient of determination(R^(2)),while the relative root mean square error(rRMSE)was employed to quantify model uncertainty.The results indicate that the scenarios with more obvious improve-ment in accuracy and effective reduction in uncertainty were Scenario 3 with the inclusion of climate and water balance information(RMSE=25.54 yr,MAE=18.03 yr,R^(2)=0.51,rRMSE=19.17%)and Scenario 5 with the inclusion of stand characterization informa-tion(RMSE=18.47 yr,MAE=13.05 yr,R^(2)=0.74,rRMSE=16.99%).Scenario 6,incorporating all feature types,achieved the highest accuracy(RMSE=17.60 yr,MAE=12.06 yr,R^(2)=0.77,rRMSE=14.19%).In this study,elevation,minimum temperature,and diameter at breast height(DBH)emerged as the key drivers of stand-age modeling.The proposed method can be used to identify drivers and to quantify uncertainty in stand-age estimation,providing a useful reference for improving model accuracy and uncertainty assessment.
基金funded by the Program of China Earthquake Science Data Sharing Platform and the Youth Fund(17404031570521)
文摘In general, the seismic response analysis in earthquake engineering assumes that the vibration parameters of the target and the contact surface of the external media are identical,i. e., single point input. However, earthquake energy has an attenuation phenomenon in wave propagation,so a wide range of soil slopes and the external medium contact surface of different input points on motion are not identical. If we consider single point input only, it may not correspond with reality, so it is necessary to carry out research on multi-point input methods. Based on the 2-D slope model,single-point input and multi-point input are performed respectively to analyze and compare their similarities and differences in the perspectives of the characteristics of seismic response of soil layer and plastic zone distribution to provide a reference for the seismic design of slopes. The results show that in the perspective of soil seismic response analysis,the peak acceleration output and peak velocity output under multi-point input are greater than the peak values under single point input at the same monitoring point,the peak appearing time is also earlier than that of the single point input; in terms of the plastic zone distribution,the multi-point effect is manifested as the presence of more obvious tensile shear failures; in the perspective of safety coefficient,the safety coefficient under each multi-point input is smaller than that of single point input,a difference of about 7 % or so. In summary,multi-point input is more reasonable and practical than single point input,so multi-point input should be considered in seismic design.
文摘Purpose – Straightness measurement of rail weld joint is of essential importance to railway maintenance. Dueto the lack of efficient measurement equipment, there has been limited in-depth research on rail weld joint with a5-m wavelength range, leaving a significant knowledge gap in this field.Design/methodology/approach – In this study, the authors used the well-established inertial referencemethod (IR-method), and the state-of-the-art multi-point chord reference method (MCR-method). Two methodshave been applied in different types of rail straightness measurement trollies, respectively. These instrumentswere tested in a high-speed rail section within a certain region of China. The test results were ultimatelyvalidated through using traditional straightedge and feeler gauge methods as reference data to evaluate the railweld joint straightness within the 5-m wavelength range.Findings – The research reveals that IR-method and MCR-method produce reasonably similar measurementresults for wavelengths below 1 m. However, MCR-method outperforms IR-method in terms of accuracy forwavelengths exceeding 3 m. Furthermore, it was observed that IR-method, while operating at a slower speed,carries the risk of derailing and is incapable of detecting rail weld joints and low joints within the track.Originality/value – The research compare two methods’ measurement effects in a longer wavelength rangeand demonstrate the superiority of MCR-method.
基金supported by National Natural Science Foundation of China(No.52176122).
文摘The centroid coordinate serves as a critical control parameter in motion systems,including aircraft,missiles,rockets,and drones,directly influencing their motion dynamics and control performance.Traditional methods for centroid measurement often necessitate custom equipment and specialized positioning devices,leading to high costs and limited accuracy.Here,we present a centroid measurement method that integrates 3D scanning technology,enabling accurate measurement of centroid across various types of objects without the need for specialized positioning fixtures.A theoretical framework for centroid measurement was established,which combined the principle of the multi-point weighing method with 3D scanning technology.The measurement accuracy was evaluated using a designed standard component.Experimental results demonstrate that the discrepancies between the theoretical and the measured centroid of a standard component with various materials and complex shapes in the X,Y,and Z directions are 0.003 mm,0.009 mm,and 0.105 mm,respectively,yielding a spatial deviation of 0.106 mm.Qualitative verification was conducted through experimental validation of three distinct types.They confirmed the reliability of the proposed method,which allowed for accurate centroid measurements of various products without requiring positioning fixtures.This advancement significantly broadened the applicability and scope of centroid measurement devices,offering new theoretical insights and methodologies for the measurement of complex parts and systems.
基金supported by the National Key R&D Program of China[grant numbers 2017YFC1501803 and 2017YFC1502102].
文摘Fast and accurate identification of unknown pollution sources plays a crucial role in the emergency response and source control of air pollution.In this work,the applicability of a previously proposed two-step inversion method is investigated with sensitivity experiments and real data from the first release of the European Tracer Experiment(ETEX-1).The two-step inversion method is based on the principle of least squares and carries out additional model correction through the residual iterative process.To evaluate its performance,its retrieval results are compared with those of two other existing algorithms.It is shown that for those cases with richer measurements,all three methods are less sensitive to errors,while for cases where measurements are sparse,their retrieval accuracy will rapidly decrease as errors increase.From the results of sensitivity experiments,the new method provides higher estimation accuracy and a more stable performance than the other two methods.The new method presents the smallest maximum location error of 18.20 km when the amplitude of the measurement error increases to 100%,and 22.67 km when errors in the wind fields increase to 200%.Moreover,when applied to ETEX-1 data,the new method also exhibits good performance,with a location error of 4.71 km,which is the best estimation with respect to source location.
基金supported by the Innovation Foundation of Provincial Education Department of Gansu(2024B-005)the Gansu Province National Science Foundation(22YF7GA182)the Fundamental Research Funds for the Central Universities(No.lzujbky2022-kb01)。
文摘Modal parameters can accurately characterize the structural dynamic properties and assess the physical state of the structure.Therefore,it is particularly significant to identify the structural modal parameters according to the monitoring data information in the structural health monitoring(SHM)system,so as to provide a scientific basis for structural damage identification and dynamic model modification.In view of this,this paper reviews methods for identifying structural modal parameters under environmental excitation and briefly describes how to identify structural damages based on the derived modal parameters.The paper primarily introduces data-driven modal parameter recognition methods(e.g.,time-domain,frequency-domain,and time-frequency-domain methods,etc.),briefly describes damage identification methods based on the variations of modal parameters(e.g.,natural frequency,modal shapes,and curvature modal shapes,etc.)and modal validation methods(e.g.,Stability Diagram and Modal Assurance Criterion,etc.).The current status of the application of artificial intelligence(AI)methods in the direction of modal parameter recognition and damage identification is further discussed.Based on the pre-vious analysis,the main development trends of structural modal parameter recognition and damage identification methods are given to provide scientific references for the optimized design and functional upgrading of SHM systems.
基金funded by the project of the Major Scientific and Technological Projects of CNOOC in the 14th Five-Year Plan(No.KJGG2022-0701)the CNOOC Research Institute(No.2020PFS-03).
文摘To analyze the differences in the transport and distribution of different types of proppants and to address issues such as the short effective support of proppant and poor placement in hydraulically intersecting fractures,this study considered the combined impact of geological-engineering factors on conductivity.Using reservoir production parameters and the discrete elementmethod,multispherical proppants were constructed.Additionally,a 3D fracture model,based on the specified conditions of the L block,employed coupled(Computational Fluid Dynamics)CFD-DEM(Discrete ElementMethod)for joint simulations to quantitatively analyze the transport and placement patterns of multispherical proppants in intersecting fractures.Results indicate that turbulent kinetic energy is an intrinsic factor affecting proppant transport.Moreover,the efficiency of placement and migration distance of low-sphericity quartz sand constructed by the DEM in the main fracture are significantly reduced compared to spherical ceramic proppants,with a 27.7%decrease in the volume fraction of the fracture surface,subsequently affecting the placement concentration and damaging fracture conductivity.Compared to small-angle fractures,controlling artificial and natural fractures to expand at angles of 45°to 60°increases the effective support length by approximately 20.6%.During hydraulic fracturing of gas wells,ensuring the fracture support area and post-closure conductivity can be achieved by controlling the sphericity of proppants and adjusting the perforation direction to control the direction of artificial fractures.
文摘We consider a uniform finite difference method for nonlinear singularly perturbed multi-point boundary value problem on Shishkin mesh. The problem is discretized using integral identities, interpolating quadrature rules, exponential basis functions and remainder terms in integral form. We show that this method is the first order convergent in the discrete maximum norm for original problem (independent of the perturbation parameter ε). To illustrate the theoretical results, we solve test problem and we also give the error distributions in the solution in Table 1 and Figures 1-3.
