Wind speed is a crucial parameter affecting wind energy utilization.However,its volatility leads to time-varying power output.Herein,a novel Seq2Seq model integrating deep learning,data denoising,and a shape-aware los...Wind speed is a crucial parameter affecting wind energy utilization.However,its volatility leads to time-varying power output.Herein,a novel Seq2Seq model integrating deep learning,data denoising,and a shape-aware loss function is proposed for accurate multistep wind speed forecasting.In this model,the wind speed data is first denoised using the maximal overlap discrete wavelet transform.Next,an encoder-decoder network based on a temporal convolutional network,bidirectional gated recurrent unit,and multihead self-attention is employed for forecasting.Additionally,to enhance the ability of the model to identify temporal dynamics,a shape-aware loss function,ITILDE-Q,is employed in the model.To verify the effectiveness of the proposed model,a comparative experiment and an ablation experiment were conducted using three datasets of measured wind speeds.Three error metrics and a similarity metric were adopted for comprehensive evaluation.The experimental results showed that the proposed model consistently outperforms benchmark models in all tested forecasting scenarios,with particularly pronounced differences in performance over longer forecast horizons.Furthermore,the synergistic interaction of the three key components contributes to the extraordinary performance of the proposed model.展开更多
The flexible rolling process(FRP) is a novel three-dimensional(3 D) forming process that combines the multipoint and traditional rolling forming. The principle of FRP is based on thickness thinning, so the deformation...The flexible rolling process(FRP) is a novel three-dimensional(3 D) forming process that combines the multipoint and traditional rolling forming. The principle of FRP is based on thickness thinning, so the deformation path significantly impacts the forming effect. In this study, the multistep forming process with different deformation paths was introduced to improve the forming effect of FRP. For instance, with the convex surface part, three finite element models of multistep FRP(MSFRP) were established. The corresponding numerical simulations and forming experiments performed among different deformation paths showed the surface part with a longer effective forming region was obtained and the forming regions with more steps in MSFRP were smoother. Thus, the sheet-metal utilization rate was greatly improved. Moreover, the MSFRP can improve the longitudinal bending effect dramatically and thereby endowing the forming part with a better forming effect. Therefore, MSFRP is a prospective method for broad applications.展开更多
We describe a rare case of the transformation of a dysplastic nodule into well-differentiated hepato- cellular carcinoma (HCC) in a 56-year-old man with alcoholrelated liver cirrhosis. Ultrasound (US) disclosed a 10 m...We describe a rare case of the transformation of a dysplastic nodule into well-differentiated hepato- cellular carcinoma (HCC) in a 56-year-old man with alcoholrelated liver cirrhosis. Ultrasound (US) disclosed a 10 mm hypoechoic nodule and contrast enhanced US revealed a hypovascular nodule, both in segment seven. US-guided biopsy revealed a high-grade dysplastic nodule characterized by enhanced cellularity with a high N/C ratio, increased cytoplasmic eosinophilia, and slight cell atypia. One year later, the US pattern of the nodule changed from hypoechoic to hyperechoic without any change in size or hypovascularity. US-guided biopsy revealed well-differentiated HCC of the same features as shown in the first biopsy, but with additional pseudoglandular formation and moderate cell atypia. Moreover, immunohistochemical staining of cyclase- associated protein 2, a new molecular marker of well- differentiated HCC, turned positive. This is the first case of multistep hepatocarcinogenesis from a dysplastic nodule to well-differentiated HCC within one year in alcohol-related liver cirrhosis.展开更多
This paper deals with the stability of linear multistep methods for multidimensional differential systems with distributed delays. The delay-dependent stability of linear multistep methods with compound quadrature rul...This paper deals with the stability of linear multistep methods for multidimensional differential systems with distributed delays. The delay-dependent stability of linear multistep methods with compound quadrature rules is studied. Several new sufficient criteria of delay-dependent stability are obtained by means of the argument principle. An algorithm is provided to check delay-dependent stability. An example that illustrates the effectiveness of the derived theoretical results is given.展开更多
This study aims to disclose the thermo-oxidative degradation behaviors and kinetics of a carbon fiber reinforced polyimide(CFRPI)composite for modeling of the Iong-term degradation process.The degradation behaviors we...This study aims to disclose the thermo-oxidative degradation behaviors and kinetics of a carbon fiber reinforced polyimide(CFRPI)composite for modeling of the Iong-term degradation process.The degradation behaviors were revealed through off-gas products analysis,and the overall kinetic interpretation was achieved from study of the mass-loss curves recorded under dynamic conditions.It was found that thermooxidative degradati on of the CFRPI composite was a multistep process,which in eluded four main reaction steps.Since most kinetic an alysis methods were derived from simple reactions described by a single kinetic triplet,they cannot be applied reliably to such a process.Therefore,we firstly separated the four overlapped reaction steps by peak fitting of derivative thermogravimetric curves using Fraser-Suzuki equation consider!ng the asymmetrical n ature of kin etic curves,and subsequently an a lyzed each in dividual reaction employing Friedma n method and experimental master-plots method.Four sets of kinetic triplets were determined to characterize the entire degradation process.The validity of four corresponding kinetic triplets was confirmed by perfect simulation of mass-loss curves recorded at both dynamic conditions used in kinetic analysis and entirely different isothermal conditions.Finally,modeling of Iong-term aging at 400°C of the CFRPI composite was successfully achieved based on these kinetic triplets.The predicted mass loss and flexural property correlated well with experimental results.This study can serve as a basis for rapid evaluation of the long-term durability of the CFRPI composite in various application environments.展开更多
The stability analysis of linear multistep methods for the numerical solutions of the systems of generalized neutral delay differential equations is discussed. The stability behaviour of linear multistep methods was a...The stability analysis of linear multistep methods for the numerical solutions of the systems of generalized neutral delay differential equations is discussed. The stability behaviour of linear multistep methods was analysed for the solution of the generalized system of linear neutral test equations, After the establishment of a sufficient condition for asymptotic stability of the solutions of the generalized system, it is shown that a linear multistep method is NGP(G)-stable if and only if it is A-stable.展开更多
In this paper,a multistep finite difference scheme has been proposed,whose coefficients are determined taking into consideration compatibility and generalized quadratic conservation,as well as incorporating historical...In this paper,a multistep finite difference scheme has been proposed,whose coefficients are determined taking into consideration compatibility and generalized quadratic conservation,as well as incorporating historical observation data.The schemes have three advantages:high-order accuracy in time,generalized square conservation,and smart use of historical observations.Numerical tests based on the one-dimensional linear advection equations suggest that reasonable consideration of accuracy,square conservation,and inclusion of historical observations is critical for good performance of a finite difference scheme.展开更多
In this study, potential of Least Square-Support Vector Regression (LS-SVR) approach is utilized to model the daily variation of river flow. Inherent complexity, unavailability of reasonably long data set and heteroge...In this study, potential of Least Square-Support Vector Regression (LS-SVR) approach is utilized to model the daily variation of river flow. Inherent complexity, unavailability of reasonably long data set and heterogeneous catchment response are the couple of issues that hinder the generalization of relationship between previous and forthcoming river flow magnitudes. The problem complexity may get enhanced with the influence of upstream dam releases. These issues are investigated by exploiting the capability of LS-SVR–an approach that considers Structural Risk Minimization (SRM) against the Empirical Risk Minimization (ERM)–used by other learning approaches, such as, Artificial Neural Network (ANN). This study is conducted in upper Narmada river basin in India having Bargi dam in its catchment, constructed in 1989. The river gauging station–Sandia is located few hundred kilometer downstream of Bargi dam. The model development is carried out with pre-construction flow regime and its performance is checked for both pre- and post-construction of the dam for any perceivable difference. It is found that the performances are similar for both the flow regimes, which indicates that the releases from the dam at daily scale for this gauging site may be ignored. In order to investigate the temporal horizon over which the prediction performance may be relied upon, a multistep-ahead prediction is carried out and the model performance is found to be reasonably good up to 5-day-ahead predictions though the performance is decreasing with the increase in lead-time. Skills of both LS-SVR and ANN are reported and it is found that the former performs better than the latter for all the lead-times in general, and shorter lead times in particular.展开更多
The model of transient behavior of semiconductor with heat-conduction is an initial and boundary problem. Alternating-direction multistep preconditioned iterative methods and theory analyses are given in this paper. E...The model of transient behavior of semiconductor with heat-conduction is an initial and boundary problem. Alternating-direction multistep preconditioned iterative methods and theory analyses are given in this paper. Electric potential equation is approximated by mixed finite element method, concentration and heat-conduction equations are approximated by Galerkin alternating-direction multistep methods. Error estimates of optimal order in L2 are demonstrated.展开更多
The transient behavior of a semiconductor device consists of a Poisson equation for the electric potential and of two nonlinear parabolic equations for the electron density and hole density. The electric potential equ...The transient behavior of a semiconductor device consists of a Poisson equation for the electric potential and of two nonlinear parabolic equations for the electron density and hole density. The electric potential equation is discretized by a mixed finite element method. The electron and hole density equations are treated by implicit-explicit multistep finite element methods. The schemes are very efficient. The optimal order error estimates both in time and space are derived.展开更多
Dispersoid formation and microstructural evolution in an oxide dispersion-strengthened CoCrFeMnNi high-entropy alloy(HEA)using a newly designed multistep sintering process are investigated.The proposed multistep sinte...Dispersoid formation and microstructural evolution in an oxide dispersion-strengthened CoCrFeMnNi high-entropy alloy(HEA)using a newly designed multistep sintering process are investigated.The proposed multistep sintering consists of a dispersoid preforming heat treatment of as-milled 0.1 wt%Y_(2)O_(3)-CoCrFeMnNi high-entropy alloy powders at 800℃,followed by sintering at 800–1000℃ under uniaxial pressure.In the conventional single-step sintered bulk,the coarsened BCC Y_(2)O_(3)dispersoids mainly form with an incoherent interface with the HEA matrix.In contrast,finer FCC Y_(2)O_(3)dispersoids,an atypical form of Y_(2)O_(3),are formed in the matrix region after multistep sintering.Nucleation of FCC Y_(2)O_(3)disper-soids is initiated on the favorable facet,the{111}plane of the austenitic matrix,with the formation of a semi-coherent interface with the matrix during the dispersoid preforming heat treatment and it maintains its refined size even after sintering.It is found that dispersoid preforming prior to sintering appears promising to control the finer dispersoid formation and refined grain structure.展开更多
Lithium-ion hybrid capacitors(LIHCs) is a promising electrochemical energy storage devices which combines the advantages of lithium-ion batteries and capacitors.Herein,we developed a facile multistep pyrolysis method,...Lithium-ion hybrid capacitors(LIHCs) is a promising electrochemical energy storage devices which combines the advantages of lithium-ion batteries and capacitors.Herein,we developed a facile multistep pyrolysis method,prepared an amorphous structure and a high-level N-doping carbon nanotubes(NCNTs),and by removing the Co catalyst,opening the port of NCNTs,and using NCNTs as anode material.It is shows good performance due to the electrolyte ions enter into the electrode materials and facilitate the charge transfer.Furthermore,we employ the porous carbon material(APDC) as the cathode to couple with anodes of NCNTs,building a LIHCs,it shows a high energy density of 173 Wh/kg at 200 W/kg and still retains 53 Wh/kg at a high power density of 10 kW/kg within the voltage window of 0-4.0 V,as well as outstanding cyclic life keep 80% capacity after 5000 cycles.This work provides an opportunity for the preparation of NCNTs,that is as a promising high-performance anode for LIHCs.展开更多
This paper deals with the stability analysis of the linear multistep (LM) methods in the numerical solution of delay differential equations. Here we provide a qualitative stability estimates, pertiment to the classica...This paper deals with the stability analysis of the linear multistep (LM) methods in the numerical solution of delay differential equations. Here we provide a qualitative stability estimates, pertiment to the classical scalar test problem of the form y′(t)=λy(t)+μy(t-τ) with τ>0 and λ,μ are complex, by using (vartiant to) the resolvent condition of Kreiss. We prove that for A stable LM methods the upper bound for the norm of the n th power of square matrix grows linearly with the order of the matrix.展开更多
Studies the numerical stability region of linear multistep(LM) methods applied to linear test equation of the form y′(t)=ay(t)+by(t-1), t>0, y(t)=g(t)-1≤t≤0, a,b∈R, proves through delay dependent stability ...Studies the numerical stability region of linear multistep(LM) methods applied to linear test equation of the form y′(t)=ay(t)+by(t-1), t>0, y(t)=g(t)-1≤t≤0, a,b∈R, proves through delay dependent stability analysis that the intersection of stability regions of the equation and the method is not empty, in addition to approaches to the boundary of the delay differential equation(DDEs) in the limiting case of step size boundary of the stability region of linear multistep methods.展开更多
The numerical stability of linear neutral Volterra delay integral differential equations is dealt with.Under a sufficient condition such that this system with a lagging argument is asymptotically stable,it is proved t...The numerical stability of linear neutral Volterra delay integral differential equations is dealt with.Under a sufficient condition such that this system with a lagging argument is asymptotically stable,it is proved that every A-stable linear multistep method preserves the delay-independent stabil-ity of its exact solutions.Finally,some numerical experiments are given to demonstrate the main conclu-sion.展开更多
A series of sufficient and necessary conditions for the algebraic stability of multistepRunge-Kutta methods is obtained, most of which can be regarded as extension of the relevant results available for Runge-Kutta met...A series of sufficient and necessary conditions for the algebraic stability of multistepRunge-Kutta methods is obtained, most of which can be regarded as extension of the relevant results available for Runge-Kutta methods, especially, for Radau Ⅰ A, Radau Ⅱ A and Gaussian Runge-Kutta methods.展开更多
Forced and damped oscillators appear in the mathematical modelling of many problems in pure and applied sciences such as physics, engineering and celestial mechanics among others. Although the accuracy of the T-functi...Forced and damped oscillators appear in the mathematical modelling of many problems in pure and applied sciences such as physics, engineering and celestial mechanics among others. Although the accuracy of the T-functions series method is high, the calculus of their coefficients needs specific recurrences in each case. To avoid this inconvenience, the T-functions series method is transformed into a multistep method whose coefficients are calculated using recurrence procedures. These methods are convergent and have the same properties to the T-functions series method. Numerical examples already used by other authors are presented, such as a stiff problem, a Duffing oscillator and an equatorial satellite problem when the perturbation comes from zonal harmonics J2.展开更多
基金supported by the National Natural Science Foundation of China(No.52171284)。
文摘Wind speed is a crucial parameter affecting wind energy utilization.However,its volatility leads to time-varying power output.Herein,a novel Seq2Seq model integrating deep learning,data denoising,and a shape-aware loss function is proposed for accurate multistep wind speed forecasting.In this model,the wind speed data is first denoised using the maximal overlap discrete wavelet transform.Next,an encoder-decoder network based on a temporal convolutional network,bidirectional gated recurrent unit,and multihead self-attention is employed for forecasting.Additionally,to enhance the ability of the model to identify temporal dynamics,a shape-aware loss function,ITILDE-Q,is employed in the model.To verify the effectiveness of the proposed model,a comparative experiment and an ablation experiment were conducted using three datasets of measured wind speeds.Three error metrics and a similarity metric were adopted for comprehensive evaluation.The experimental results showed that the proposed model consistently outperforms benchmark models in all tested forecasting scenarios,with particularly pronounced differences in performance over longer forecast horizons.Furthermore,the synergistic interaction of the three key components contributes to the extraordinary performance of the proposed model.
基金support given by the National Natural Science Foundation of China(No.51275202)
文摘The flexible rolling process(FRP) is a novel three-dimensional(3 D) forming process that combines the multipoint and traditional rolling forming. The principle of FRP is based on thickness thinning, so the deformation path significantly impacts the forming effect. In this study, the multistep forming process with different deformation paths was introduced to improve the forming effect of FRP. For instance, with the convex surface part, three finite element models of multistep FRP(MSFRP) were established. The corresponding numerical simulations and forming experiments performed among different deformation paths showed the surface part with a longer effective forming region was obtained and the forming regions with more steps in MSFRP were smoother. Thus, the sheet-metal utilization rate was greatly improved. Moreover, the MSFRP can improve the longitudinal bending effect dramatically and thereby endowing the forming part with a better forming effect. Therefore, MSFRP is a prospective method for broad applications.
文摘We describe a rare case of the transformation of a dysplastic nodule into well-differentiated hepato- cellular carcinoma (HCC) in a 56-year-old man with alcoholrelated liver cirrhosis. Ultrasound (US) disclosed a 10 mm hypoechoic nodule and contrast enhanced US revealed a hypovascular nodule, both in segment seven. US-guided biopsy revealed a high-grade dysplastic nodule characterized by enhanced cellularity with a high N/C ratio, increased cytoplasmic eosinophilia, and slight cell atypia. One year later, the US pattern of the nodule changed from hypoechoic to hyperechoic without any change in size or hypovascularity. US-guided biopsy revealed well-differentiated HCC of the same features as shown in the first biopsy, but with additional pseudoglandular formation and moderate cell atypia. Moreover, immunohistochemical staining of cyclase- associated protein 2, a new molecular marker of well- differentiated HCC, turned positive. This is the first case of multistep hepatocarcinogenesis from a dysplastic nodule to well-differentiated HCC within one year in alcohol-related liver cirrhosis.
基金Project supported by the National Natural Science Foundation of China(No.11471217)
文摘This paper deals with the stability of linear multistep methods for multidimensional differential systems with distributed delays. The delay-dependent stability of linear multistep methods with compound quadrature rules is studied. Several new sufficient criteria of delay-dependent stability are obtained by means of the argument principle. An algorithm is provided to check delay-dependent stability. An example that illustrates the effectiveness of the derived theoretical results is given.
文摘This study aims to disclose the thermo-oxidative degradation behaviors and kinetics of a carbon fiber reinforced polyimide(CFRPI)composite for modeling of the Iong-term degradation process.The degradation behaviors were revealed through off-gas products analysis,and the overall kinetic interpretation was achieved from study of the mass-loss curves recorded under dynamic conditions.It was found that thermooxidative degradati on of the CFRPI composite was a multistep process,which in eluded four main reaction steps.Since most kinetic an alysis methods were derived from simple reactions described by a single kinetic triplet,they cannot be applied reliably to such a process.Therefore,we firstly separated the four overlapped reaction steps by peak fitting of derivative thermogravimetric curves using Fraser-Suzuki equation consider!ng the asymmetrical n ature of kin etic curves,and subsequently an a lyzed each in dividual reaction employing Friedma n method and experimental master-plots method.Four sets of kinetic triplets were determined to characterize the entire degradation process.The validity of four corresponding kinetic triplets was confirmed by perfect simulation of mass-loss curves recorded at both dynamic conditions used in kinetic analysis and entirely different isothermal conditions.Finally,modeling of Iong-term aging at 400°C of the CFRPI composite was successfully achieved based on these kinetic triplets.The predicted mass loss and flexural property correlated well with experimental results.This study can serve as a basis for rapid evaluation of the long-term durability of the CFRPI composite in various application environments.
文摘The stability analysis of linear multistep methods for the numerical solutions of the systems of generalized neutral delay differential equations is discussed. The stability behaviour of linear multistep methods was analysed for the solution of the generalized system of linear neutral test equations, After the establishment of a sufficient condition for asymptotic stability of the solutions of the generalized system, it is shown that a linear multistep method is NGP(G)-stable if and only if it is A-stable.
基金the Ministry of Science and Technology of China for funding the National Basic Research Program of China (973 Program,Grant No.2011CB309704)
文摘In this paper,a multistep finite difference scheme has been proposed,whose coefficients are determined taking into consideration compatibility and generalized quadratic conservation,as well as incorporating historical observation data.The schemes have three advantages:high-order accuracy in time,generalized square conservation,and smart use of historical observations.Numerical tests based on the one-dimensional linear advection equations suggest that reasonable consideration of accuracy,square conservation,and inclusion of historical observations is critical for good performance of a finite difference scheme.
文摘In this study, potential of Least Square-Support Vector Regression (LS-SVR) approach is utilized to model the daily variation of river flow. Inherent complexity, unavailability of reasonably long data set and heterogeneous catchment response are the couple of issues that hinder the generalization of relationship between previous and forthcoming river flow magnitudes. The problem complexity may get enhanced with the influence of upstream dam releases. These issues are investigated by exploiting the capability of LS-SVR–an approach that considers Structural Risk Minimization (SRM) against the Empirical Risk Minimization (ERM)–used by other learning approaches, such as, Artificial Neural Network (ANN). This study is conducted in upper Narmada river basin in India having Bargi dam in its catchment, constructed in 1989. The river gauging station–Sandia is located few hundred kilometer downstream of Bargi dam. The model development is carried out with pre-construction flow regime and its performance is checked for both pre- and post-construction of the dam for any perceivable difference. It is found that the performances are similar for both the flow regimes, which indicates that the releases from the dam at daily scale for this gauging site may be ignored. In order to investigate the temporal horizon over which the prediction performance may be relied upon, a multistep-ahead prediction is carried out and the model performance is found to be reasonably good up to 5-day-ahead predictions though the performance is decreasing with the increase in lead-time. Skills of both LS-SVR and ANN are reported and it is found that the former performs better than the latter for all the lead-times in general, and shorter lead times in particular.
基金This research was surpported by the National Natural Science Foundation , Mathematical TY Foun-dation (TY10126029) of China and the Youth Foundation of Shandong University.
文摘The model of transient behavior of semiconductor with heat-conduction is an initial and boundary problem. Alternating-direction multistep preconditioned iterative methods and theory analyses are given in this paper. Electric potential equation is approximated by mixed finite element method, concentration and heat-conduction equations are approximated by Galerkin alternating-direction multistep methods. Error estimates of optimal order in L2 are demonstrated.
文摘The transient behavior of a semiconductor device consists of a Poisson equation for the electric potential and of two nonlinear parabolic equations for the electron density and hole density. The electric potential equation is discretized by a mixed finite element method. The electron and hole density equations are treated by implicit-explicit multistep finite element methods. The schemes are very efficient. The optimal order error estimates both in time and space are derived.
基金supported by the National Research Foundation of the Ministry of Science and ICT(MSIT)of the Republic of Korea(Nos.2021R1A2C2014025,2020R1A5A6017701,and 2022M3H4A1A02076759)。
文摘Dispersoid formation and microstructural evolution in an oxide dispersion-strengthened CoCrFeMnNi high-entropy alloy(HEA)using a newly designed multistep sintering process are investigated.The proposed multistep sintering consists of a dispersoid preforming heat treatment of as-milled 0.1 wt%Y_(2)O_(3)-CoCrFeMnNi high-entropy alloy powders at 800℃,followed by sintering at 800–1000℃ under uniaxial pressure.In the conventional single-step sintered bulk,the coarsened BCC Y_(2)O_(3)dispersoids mainly form with an incoherent interface with the HEA matrix.In contrast,finer FCC Y_(2)O_(3)dispersoids,an atypical form of Y_(2)O_(3),are formed in the matrix region after multistep sintering.Nucleation of FCC Y_(2)O_(3)disper-soids is initiated on the favorable facet,the{111}plane of the austenitic matrix,with the formation of a semi-coherent interface with the matrix during the dispersoid preforming heat treatment and it maintains its refined size even after sintering.It is found that dispersoid preforming prior to sintering appears promising to control the finer dispersoid formation and refined grain structure.
基金supported by the Natural Science Foundation of China(No.21872066)the Natural Science Foundation of Gansu(No.18JR3RA274)。
文摘Lithium-ion hybrid capacitors(LIHCs) is a promising electrochemical energy storage devices which combines the advantages of lithium-ion batteries and capacitors.Herein,we developed a facile multistep pyrolysis method,prepared an amorphous structure and a high-level N-doping carbon nanotubes(NCNTs),and by removing the Co catalyst,opening the port of NCNTs,and using NCNTs as anode material.It is shows good performance due to the electrolyte ions enter into the electrode materials and facilitate the charge transfer.Furthermore,we employ the porous carbon material(APDC) as the cathode to couple with anodes of NCNTs,building a LIHCs,it shows a high energy density of 173 Wh/kg at 200 W/kg and still retains 53 Wh/kg at a high power density of 10 kW/kg within the voltage window of 0-4.0 V,as well as outstanding cyclic life keep 80% capacity after 5000 cycles.This work provides an opportunity for the preparation of NCNTs,that is as a promising high-performance anode for LIHCs.
文摘This paper deals with the stability analysis of the linear multistep (LM) methods in the numerical solution of delay differential equations. Here we provide a qualitative stability estimates, pertiment to the classical scalar test problem of the form y′(t)=λy(t)+μy(t-τ) with τ>0 and λ,μ are complex, by using (vartiant to) the resolvent condition of Kreiss. We prove that for A stable LM methods the upper bound for the norm of the n th power of square matrix grows linearly with the order of the matrix.
文摘Studies the numerical stability region of linear multistep(LM) methods applied to linear test equation of the form y′(t)=ay(t)+by(t-1), t>0, y(t)=g(t)-1≤t≤0, a,b∈R, proves through delay dependent stability analysis that the intersection of stability regions of the equation and the method is not empty, in addition to approaches to the boundary of the delay differential equation(DDEs) in the limiting case of step size boundary of the stability region of linear multistep methods.
基金Supported by the Natural Science Foundation of Heilongjiang Province(A200602)the Project of Science Research Foundation(HITC200710)the Project of Development Program for Outstanding Young Teachers in Harbin Institute of Technology(HITQNJS.2006.053)
文摘The numerical stability of linear neutral Volterra delay integral differential equations is dealt with.Under a sufficient condition such that this system with a lagging argument is asymptotically stable,it is proved that every A-stable linear multistep method preserves the delay-independent stabil-ity of its exact solutions.Finally,some numerical experiments are given to demonstrate the main conclu-sion.
文摘A series of sufficient and necessary conditions for the algebraic stability of multistepRunge-Kutta methods is obtained, most of which can be regarded as extension of the relevant results available for Runge-Kutta methods, especially, for Radau Ⅰ A, Radau Ⅱ A and Gaussian Runge-Kutta methods.
文摘Forced and damped oscillators appear in the mathematical modelling of many problems in pure and applied sciences such as physics, engineering and celestial mechanics among others. Although the accuracy of the T-functions series method is high, the calculus of their coefficients needs specific recurrences in each case. To avoid this inconvenience, the T-functions series method is transformed into a multistep method whose coefficients are calculated using recurrence procedures. These methods are convergent and have the same properties to the T-functions series method. Numerical examples already used by other authors are presented, such as a stiff problem, a Duffing oscillator and an equatorial satellite problem when the perturbation comes from zonal harmonics J2.
