We present the new predictor-corrector methods for systems of nonlinear differential equations, based on the method of exponential time differencing. We compare the present schemes with the explicit multistep exponent...We present the new predictor-corrector methods for systems of nonlinear differential equations, based on the method of exponential time differencing. We compare the present schemes with the explicit multistep exponential time differencing and Adams–Bashforth–Moulton method. The numerical results show that the schemes are more accurate and more efficient than Adams predictor-corrector method. The exponential time differencing method has been developed and perfected by the present studies.展开更多
We develop the three-step explicit and implicit schemes of exponential fitting methods. We use the three- step explicit exponential fitting scheme to predict an approximation, then use the three-step implicit exponent...We develop the three-step explicit and implicit schemes of exponential fitting methods. We use the three- step explicit exponential fitting scheme to predict an approximation, then use the three-step implicit exponential fitting scheme to correct this prediction. This combination is called the three-step predictor-corrector of exponential fitting method. The three-step predictor-corrector of exponential fitting method is applied to numerically compute the coupled nonlinear Schroedinger equation and the nonlinear Schroedinger equation with varying coefficients. The numerical results show that the scheme is highly accurate.展开更多
By the discussion of the formula and properties of (4,4) parametric form rational approximation to function exp(q), the fourth order derivative one_step exponentially fitted method and the third order derivative hybri...By the discussion of the formula and properties of (4,4) parametric form rational approximation to function exp(q), the fourth order derivative one_step exponentially fitted method and the third order derivative hybrid one_step exponentially fitted method are presented, their order p satisfying 6≤p≤8. The necessary and sufficient conditions for the two methods to be A_ stable are given. Finally, for the fourth order derivative method, the error bound and the necessary and sufficient conditions for it to be median are discussed.展开更多
Numerical stability when integrating plane waves of cubic SchrSdinger equation is thor- oughly analysed for some explicit exponential methods. We center on the following second- order methods： Strang splitting and La...Numerical stability when integrating plane waves of cubic SchrSdinger equation is thor- oughly analysed for some explicit exponential methods. We center on the following second- order methods： Strang splitting and Lawson method based on a one-parameter family of 2-stage 2nd-order explicit Runge-Kutta methods. Regions of stability are plotted and numerical results are shown which corroborate the theoretical results. Besides, a tech- nique is suggested to avoid the possible numerical instabilities which do not correspond to continuous ones.展开更多
The hydrological system in Central Asia is highly sensitive to global climate change,significantly affecting water supply and energy production.In Tajikistan,the Vakhsh River—one of the main tributaries of the Amu Da...The hydrological system in Central Asia is highly sensitive to global climate change,significantly affecting water supply and energy production.In Tajikistan,the Vakhsh River—one of the main tributaries of the Amu Darya—plays a key role in the region’s hydropower and irrigation.However,research on long-term hydrological changes in its two top large basins—the Surkhob and Khingov river basins—remains limited.Therefore,this study analyzed long-term climate and hydrological changes in the Vakhsh River,including its main tributaries—the Surkhob and Khingov rivers—which are vital for the water resource management in Tajikistan and even in Central Asia.Using long-term hydrometeorological observations,the change trends of temperature(1933–2020),precipitation(1970–2020),and runoff(1940–2018)were examined to assess the impact of climate change on the regional water resources.The analysis revealed the occurrence of significant warming and a spatially uneven increase in precipitation.The temperature changes across three climatic periods(1933–1960,1960–1990,and 1990–2020)indicated that there was a transition from baseline level to accelerated warming.The precipitation showed a 2.99 mm/a increase in the Khingov River Basin and a 2.80 mm/a increase in the Surkhob River Basin during 1970–2020.Moreover,there was a gradual shift toward wetter conditions in recent decades.Despite the relatively stable annual mean runoff,seasonal redistribution occurred,with increased runoff in spring and reduced runoff in summer,due to the compensation of glacier melting.Moreover,this study forecasted runoff change during 2019–2040 using the exponential triple smoothing(ETS)method and revealed the occurrence of alternating wet and dry phases,emphasizing the sensitivity of the Vakhsh River Basin’s hydrological system to climate change and the necessity of adaptive water resource management in mountainous regions of Central Asia.Therefore,this study can provide evidence-based insights that are critical for future water resources planning,climate-resilient hydropower development,and regional adaptation strategies in climate-vulnerable basins in Central Asia.展开更多
An improved precise integration method （IPIM） for solving the differential Riccati equation （DRE） is presented. The solution to the DRE is connected with the exponential of a Hamiltonian matrix, and the precise in...An improved precise integration method （IPIM） for solving the differential Riccati equation （DRE） is presented. The solution to the DRE is connected with the exponential of a Hamiltonian matrix, and the precise integration method （PIM） for solving the DRE is connected with the scaling and squaring method for computing the exponential of a matrix. The error analysis of the scaling and squaring method for the exponential of a matrix is applied to the PIM of the DRE. Based ,on the error analysis, the criterion for choosing two parameters of the PIM is given. Three kinds of IPIMs for solving the DRE are proposed. The numerical examples machine accuracy solutions. show that the IPIM is stable and gives the展开更多
The absorption coefficient of water is an important bio-optical parameter for water optics and water color remote sensing. However, scattering correction is essential to obtain accurate absorption coefficient values i...The absorption coefficient of water is an important bio-optical parameter for water optics and water color remote sensing. However, scattering correction is essential to obtain accurate absorption coefficient values in situ using the nine-wavelength absorption and attenuation meter AC9. Establishing the correction always fails in Case 2 water when the correction assumes zero absorption in the near-infrared(NIR) region and underestimates the absorption coefficient in the red region, which affect processes such as semi-analytical remote sensing inversion. In this study, the scattering contribution was evaluated by an exponential fitting approach using AC9 measurements at seven wavelengths(412, 440, 488, 510, 532, 555, and 715 nm) and by applying scattering correction. The correction was applied to representative in situ data of moderately turbid coastal water, highly turbid coastal water, eutrophic inland water, and turbid inland water. The results suggest that the absorption levels in the red and NIR regions are significantly higher than those obtained using standard scattering error correction procedures. Knowledge of the deviation between this method and the commonly used scattering correction methods will facilitate the evaluation of the effect on satellite remote sensing of water constituents and general optical research using different scatteringcorrection methods.展开更多
This study proposes a three-dimensional(3D)coupled magneto-electro-elastic problem for the static analysis of multilayered plates embedding piezomagnetic and piezoelectric layers by considering both sensor and actuato...This study proposes a three-dimensional(3D)coupled magneto-electro-elastic problem for the static analysis of multilayered plates embedding piezomagnetic and piezoelectric layers by considering both sensor and actuator configurations.The 3D governing equations for the magneto-electro-elastic static behavior of plates are explicitly show that are made by the three 3D equilibrium equations,the 3D divergence equation for magnetic induction,and the 3D divergence equation for the electric displacement.The proposed solution involves the exponential matrix in the thickness direction and primary variables’harmonic forms in the in-plane ones.A closed-form solution is performed considering simply-supported boundary conditions.Interlaminar continuity conditions are imposed for displacements,magnetic potential,electric potential,transverse shear/normal stresses,transverse normal magnetic induction and transverse normal electric displacement.Therefore,a layerwise approach is adopted.The results section is composed of an assessment part,where the present model is compared to past 3D electro-elastic or magneto-elastic formulations and a new benchmark part.Benchmarks consider sensor and actuator plate configurations for the fully coupled magneto-electro-elastic cases for different thickness ratios.Tabular and graphical results are presented for displacements,stresses,magnetic potential,electric potential,transverse normal magnetic induction and transverse normal electric displacement.For each presented benchmark,magneto-electro-elastic coupling and thickness and material layer effects are discussed in depth.展开更多
In this paper,we formulate two new families of fourth-order explicit exponential Runge–Kutta(ERK)methods with four stages for solving first-order differential systems y'(t)+M y(t)=f(y(t)).The order conditions of ...In this paper,we formulate two new families of fourth-order explicit exponential Runge–Kutta(ERK)methods with four stages for solving first-order differential systems y'(t)+M y(t)=f(y(t)).The order conditions of these ERK methods are derived by comparing the Taylor series of the exact solution,which are exactly identical to the order conditions of explicit Runge–Kutta methods,and these ERK methods reduce to classical Runge–Kutta methods once M→0.Moreover,we analyze the stability properties and the convergence of these new methods.Several numerical examples are implemented to illustrate the accuracy and efficiency of these ERK methods by comparison with standard exponential integrators.展开更多
A three-dimensional(3D)analytical formulation is proposed to put together magnetic,electric and elastic fields to analyze the vibration modes of simply-supported layered piezo-electro-magnetic plates.The present 3D mo...A three-dimensional(3D)analytical formulation is proposed to put together magnetic,electric and elastic fields to analyze the vibration modes of simply-supported layered piezo-electro-magnetic plates.The present 3D model allows analyses for layered smart plates in both open-circuit and closed-circuit configurations.The secondorder differential equations written in the mixed curvilinear reference system govern the magneto-electro-elastic free vibration problem for multilayered plates.This set consists of the 3D equations of motion and the 3D divergence equations for the magnetic induction and electric displacement.Navier harmonic forms in the planar directions and the exponential matrix method in the transversal direction of the plate are applied to solve the second-order differential equations in terms of displacements.For these reasons,simply-supported boundary conditions are considered.Imposition of interlaminar continuity conditions on primary variables(displacements,magnetic potential,electric potential),and some secondary variables(transverse normal and transverse shear stresses,transverse normal magnetic induction/electric displacement)allows the implementation of the layer-wise approach.Assessments for both load boundary configurations are proposed in the results section to validate the present 3D approach.3D electro-elastic and 3D magneto-elastic coupling validations are performed separately considering different models from the open literature.A new benchmark involving a full magneto-electro-elastic coupling for multilayered plates is presented considering both load boundary configurations for different thickness ratios.For this benchmark,circular frequency values and related vibration modes through the transverse direction in terms of displacements,magnetic and electric potential,transverse normal magnetic induction/electric displacement are shown to visualize the magneto-electroelastic coupling and material and thickness layer effects.The present formulation has been entirely implemented in an academic Matlab(R2024a)code developed by the authors.In this paper,for the first time,the second-order differential equations governing the magneto-electro-elastic problem for the free vibration analysis of plates has been solved considering the mixed mode of harmonic forms and exponential matrix.The exponential matrix permits computing the secondary variable of the problem(stresses,electric displacement components and magnetic induction components)exactly,directly from constitutive and geometrical equations.In addition,the very simple and elegant formulation permits having a code with very low computational costs.The present manuscript aims to fill the void in open literature regarding reference 3D solutions for the free vibration analysis of magneto-electro-elastic plates.展开更多
In a previous paper,a technique was suggested to avoid order reduction with any explicit exponential Runge-Kutta method when integrating initial boundary value nonlinear problems with time-dependent boundary condition...In a previous paper,a technique was suggested to avoid order reduction with any explicit exponential Runge-Kutta method when integrating initial boundary value nonlinear problems with time-dependent boundary conditions.In this paper,we significantly simplify the full discretization formulas to be applied under conditions which are nearly always satisfied in practice.Not only a simpler linear combination of'j-functions is given for both the stages and the solution,but also the information required on the boundary is so much simplified that,in order to get local order three,it is no longer necessary to resort to numerical differentiation in space.In many cases,even to get local order 4.The technique is then shown to be computationally competitive against other widely used methods with high enough stiff order through the standard method of lines.展开更多
In this paper,we develop a general framework for constructing higher-order,unconditionally energydecreasing exponential time differencing Runge-Kutta(ETDRK)methods applicable to a range of gradient flows.Specifically,...In this paper,we develop a general framework for constructing higher-order,unconditionally energydecreasing exponential time differencing Runge-Kutta(ETDRK)methods applicable to a range of gradient flows.Specifically,we identify conditions sufficient for ETDRK schemes to maintain the original energy dissipation.Our analysis reveals that the widely-employed third-and fourth-order ETDRK schemes fail to meet these conditions.To address this,we introduce new third-order ETDRK schemes,designed with appropriate stabilization,which satisfy these conditions and thus guarantee the unconditional energy decay property.We conduct extensive numerical experiments with these new schemes to verify their accuracy,stability,behavior under large time steps,long-term evolution,and adaptive time-stepping strategy across various gradient flows.This study offers the first framework to examine the unconditional energy stability of high-order ETDRK methods,and we are optimistic that our framework will enable the development of ETDRK schemes beyond the third order that are unconditionally energy stable.展开更多
The present paper deals with the Sharma-Tasso-Olver-Burgers equation(STOBE)and its conservation laws and kink solitons.More precisely,the formal Lagrangian,Lie symmetries,and adjoint equations of the STOBE are firstly...The present paper deals with the Sharma-Tasso-Olver-Burgers equation(STOBE)and its conservation laws and kink solitons.More precisely,the formal Lagrangian,Lie symmetries,and adjoint equations of the STOBE are firstly constructed to retrieve its conservation laws.Kink solitons of the STOBE are then extracted through adopting a series of newly well-designed approaches such as Kudryashov and exponential methods.Diverse graphs in 2 and 3D postures are formally portrayed to reveal the dynamical features of kink solitons.According to the authors’knowledge,the outcomes of the current investigation are new and have been listed for the first time.展开更多
In this paper,we mainly study an inverse source problem of time fractional diffusion equation in a bounded domain with an over-specified terminal condition at a fixed time.A novel regularization method,which we call t...In this paper,we mainly study an inverse source problem of time fractional diffusion equation in a bounded domain with an over-specified terminal condition at a fixed time.A novel regularization method,which we call the exponential Tikhonov regularization method with a parameter γ,is proposed to solve the inverse source problem,and the corresponding convergence analysis is given under a-priori and a-posteriori regularization parameter choice rules.Whenγis less than or equal to zero,the optimal convergence rate can be achieved and it is independent of the value of γ.However,when γ is greater than zero,the optimal convergence rate depends on the value of γ which is related to the regularity of the unknown source.Finally,numerical experiments are conducted for showing the effectiveness of the proposed exponential regularization method.展开更多
The prime objective of this paper is to explore the new exact soliton solutions to the higher-dimensional nonlinear Fokas equation and(2+1)-dimensional breaking soliton equations via a generalized exponential rational...The prime objective of this paper is to explore the new exact soliton solutions to the higher-dimensional nonlinear Fokas equation and(2+1)-dimensional breaking soliton equations via a generalized exponential rational function(GERF) method. Many different kinds of exact soliton solution are obtained, all of which are completely novel and have never been reported in the literature before. The dynamical behaviors of some obtained exact soliton solutions are also demonstrated by a choice of appropriate values of the free constants that aid in understanding the nonlinear complex phenomena of such equations. These exact soliton solutions are observed in the shapes of different dynamical structures of localized solitary wave solutions, singular-form solitons, single solitons,double solitons, triple solitons, bell-shaped solitons, combo singular solitons, breather-type solitons,elastic interactions between triple solitons and kink waves, and elastic interactions between diverse solitons and kink waves. Because of the reduction in symbolic computation work and the additional constructed closed-form solutions, it is observed that the suggested technique is effective, robust, and straightforward. Moreover, several other types of higher-dimensional nonlinear evolution equation can be solved using the powerful GERF technique.展开更多
In this paper, a novel class of exponential Fourier collocation methods （EFCMs） is presented for solving systems of first-order ordinary differential equations. These so-called exponential Fourier collocation method...In this paper, a novel class of exponential Fourier collocation methods （EFCMs） is presented for solving systems of first-order ordinary differential equations. These so-called exponential Fourier collocation methods are based on the variation-of-constants formula, incorporating a local Fourier expansion of the underlying problem with collocation meth- ods. We discuss in detail the connections of EFCMs with trigonometric Fourier colloca- tion methods （TFCMs）, the well-known Hamiltonian Boundary Value Methods （HBVMs）, Gauss methods and Radau IIA methods. It turns out that the novel EFCMs are an es- sential extension of these existing methods. We also analyse the accuracy in preserving the quadratic invariants and the Hamiltonian energy when the underlying system is a Hamiltonian system. Other properties of EFCMs including the order of approximations and the convergence of fixed-point iterations are investigated as well. The analysis given in this paper proves further that EFCMs can achieve arbitrarily high order in a routine manner which allows us to construct higher-order methods for solving systems of first- order ordinary differential equations conveniently. We also derive a practical fourth-order EFCM denoted by EFCM（2,2） as an illustrative example. The numerical experiments using EFCM（2,2） are implemented in comparison with an existing fourth-order HBVM, an energy-preserving collocation method and a fourth-order exponential integrator in the literature. The numerical results demonstrate the remarkable efficiency and robustness of the novel EFCM（2,2）.展开更多
This paper generalizes the exponential Runge-Kutta asymptotic preserving(AP)method developed in[G.Dimarco and L.Pareschi,SIAM Numer.Anal.,49(2011),pp.2057–2077]to compute the multi-species Boltzmann equation.Compared...This paper generalizes the exponential Runge-Kutta asymptotic preserving(AP)method developed in[G.Dimarco and L.Pareschi,SIAM Numer.Anal.,49(2011),pp.2057–2077]to compute the multi-species Boltzmann equation.Compared to the single species Boltzmann equation that the method was originally applied on,this set of equation presents a new difficulty that comes from the lack of local conservation laws due to the interaction between different species.Hence extra stiff nonlinear source terms need to be treated properly to maintain the accuracy and the AP property.The method we propose does not contain any nonlinear nonlocal implicit solver,and can capture the hydrodynamic limit with time step and mesh size independent of the Knudsen number.We prove the positivity and strong AP properties of the scheme,which are verified by two numerical examples.展开更多
Throughput prediction is essential for congestion control and LTE network management. In this paper, the autoregressive integrated moving average （ARIMA） model and exponential smoothing model are used to predict the...Throughput prediction is essential for congestion control and LTE network management. In this paper, the autoregressive integrated moving average （ARIMA） model and exponential smoothing model are used to predict the throughput in a single cell and whole region in an LTE network. The experimental results show that these two models perform differently in both scenarios. The ARIMA model is better than the exponential smoothing model for predicting throughput on weekdays in a whole region. The exponential smoothing model is better than the ARIMA model for predicting throughput on weekends in a whole region. The exponential smoothing model is better than the ARIMA model for predicting throughput in a single cell. In these two LTE network scenarios, throughput prediction based on traffic time series leads to more efficient resource management and better QoS.展开更多
An efficient and accurate exponential wave integrator Fourier pseudospectral （EWI-FP） method is proposed and analyzed for solving the symmetric regularized-long-wave （SRLW） equation, which is used for modeling the...An efficient and accurate exponential wave integrator Fourier pseudospectral （EWI-FP） method is proposed and analyzed for solving the symmetric regularized-long-wave （SRLW） equation, which is used for modeling the weakly nonlinear ion acoustic and space-charge waves. The numerical method here is based on a Gautschi-type exponential wave integrator for temporal approximation and the Fourier pseudospectral method for spatial discretization. The scheme is fully explicit and efficient due to the fast Fourier transform. Numerical analysis of the proposed EWI-FP method is carried out and rigorous error estimates are established without CFL-type condition by means of the mathematical induction. The error bound shows that EWI-FP has second order accuracy in time and spectral accuracy in space. Numerical results are reported to confirm the theoretical studies and indicate that the error bound here is optimal.展开更多
Research on heat and mass flux yielded by modern seafloor hydrothermal activity is very important, because it is involved not only in the base of ocean environment research, but also in the historical evolution of sea...Research on heat and mass flux yielded by modern seafloor hydrothermal activity is very important, because it is involved not only in the base of ocean environment research, but also in the historical evolution of seawater properties. Currently, estimating heat flux is based on the observation data of hydrothermal smokers, low-temperature diffusive flow and mid-ocean ridge mainly. But there are some faults, for example, there is lack of a concurrent conductive item in estimating the heat flux by smokers and the error between the half-space cooling model and the observation data is too large. So, three kinds of methods are applied to re-estimating the heat flux of hydrothermal activity resepectively, corresponding estimation is 97. 359 GW by hydrothermal smoker and diffusive flow, 84.895 GW by hydrothermal plume, and 4. 11 TW by exponential attenuation method put forward by this paper. Research on mass flux estimation is relatively rare, the main reason for this is insufficient field observation data. Mass fluxes of different elements are calculated using hydrothermal vent fluid data from the TAG hydrothermal area on the Mid-Atlantic Ridge for the first time. Difference of estimations by different methods reflects the researching extent of hydrothermal activity, and systematically in - situ observation will help to estimate the contribution of hydrothermal activity to ocean chemical environment, ocean circulation and global climate precisely.展开更多
基金The project supported by National Natural Science Foundation of China under Grant No.19902002
文摘We present the new predictor-corrector methods for systems of nonlinear differential equations, based on the method of exponential time differencing. We compare the present schemes with the explicit multistep exponential time differencing and Adams–Bashforth–Moulton method. The numerical results show that the schemes are more accurate and more efficient than Adams predictor-corrector method. The exponential time differencing method has been developed and perfected by the present studies.
基金The project supported by Liu Hui Applied Mathematics Center of Nankai University and 985 Education Development Plan of Tianjin University
文摘We develop the three-step explicit and implicit schemes of exponential fitting methods. We use the three- step explicit exponential fitting scheme to predict an approximation, then use the three-step implicit exponential fitting scheme to correct this prediction. This combination is called the three-step predictor-corrector of exponential fitting method. The three-step predictor-corrector of exponential fitting method is applied to numerically compute the coupled nonlinear Schroedinger equation and the nonlinear Schroedinger equation with varying coefficients. The numerical results show that the scheme is highly accurate.
基金the Science Technology Foundation of Ministry of Machine_ Buildin
文摘By the discussion of the formula and properties of (4,4) parametric form rational approximation to function exp(q), the fourth order derivative one_step exponentially fitted method and the third order derivative hybrid one_step exponentially fitted method are presented, their order p satisfying 6≤p≤8. The necessary and sufficient conditions for the two methods to be A_ stable are given. Finally, for the fourth order derivative method, the error bound and the necessary and sufficient conditions for it to be median are discussed.
文摘Numerical stability when integrating plane waves of cubic SchrSdinger equation is thor- oughly analysed for some explicit exponential methods. We center on the following second- order methods： Strang splitting and Lawson method based on a one-parameter family of 2-stage 2nd-order explicit Runge-Kutta methods. Regions of stability are plotted and numerical results are shown which corroborate the theoretical results. Besides, a tech- nique is suggested to avoid the possible numerical instabilities which do not correspond to continuous ones.
基金supported by the National Natural Science Foundation of China(W2412135).
文摘The hydrological system in Central Asia is highly sensitive to global climate change,significantly affecting water supply and energy production.In Tajikistan,the Vakhsh River—one of the main tributaries of the Amu Darya—plays a key role in the region’s hydropower and irrigation.However,research on long-term hydrological changes in its two top large basins—the Surkhob and Khingov river basins—remains limited.Therefore,this study analyzed long-term climate and hydrological changes in the Vakhsh River,including its main tributaries—the Surkhob and Khingov rivers—which are vital for the water resource management in Tajikistan and even in Central Asia.Using long-term hydrometeorological observations,the change trends of temperature(1933–2020),precipitation(1970–2020),and runoff(1940–2018)were examined to assess the impact of climate change on the regional water resources.The analysis revealed the occurrence of significant warming and a spatially uneven increase in precipitation.The temperature changes across three climatic periods(1933–1960,1960–1990,and 1990–2020)indicated that there was a transition from baseline level to accelerated warming.The precipitation showed a 2.99 mm/a increase in the Khingov River Basin and a 2.80 mm/a increase in the Surkhob River Basin during 1970–2020.Moreover,there was a gradual shift toward wetter conditions in recent decades.Despite the relatively stable annual mean runoff,seasonal redistribution occurred,with increased runoff in spring and reduced runoff in summer,due to the compensation of glacier melting.Moreover,this study forecasted runoff change during 2019–2040 using the exponential triple smoothing(ETS)method and revealed the occurrence of alternating wet and dry phases,emphasizing the sensitivity of the Vakhsh River Basin’s hydrological system to climate change and the necessity of adaptive water resource management in mountainous regions of Central Asia.Therefore,this study can provide evidence-based insights that are critical for future water resources planning,climate-resilient hydropower development,and regional adaptation strategies in climate-vulnerable basins in Central Asia.
基金Project supported by the National Natural Science Foundation of China(Nos.10902020 and 10721062)
文摘An improved precise integration method （IPIM） for solving the differential Riccati equation （DRE） is presented. The solution to the DRE is connected with the exponential of a Hamiltonian matrix, and the precise integration method （PIM） for solving the DRE is connected with the scaling and squaring method for computing the exponential of a matrix. The error analysis of the scaling and squaring method for the exponential of a matrix is applied to the PIM of the DRE. Based ,on the error analysis, the criterion for choosing two parameters of the PIM is given. Three kinds of IPIMs for solving the DRE are proposed. The numerical examples machine accuracy solutions. show that the IPIM is stable and gives the
基金Supported by the National Key Research and Development Program of China(Nos.2016YFB0501502,2016YFC1400903,2016YFB0500304)the National Natural Science Foundation of China(Nos.91638201,41276184,41325004,41471308,41571361)+1 种基金the High Resolution Earth Observation Systems of National Science and Technology Major Projects(No.41-Y20A31-9003-15/17)the Director Foundation of Institute of Remote Sensing and Digital Earth,Chinese Academy of Sciences(No.Y6SJ2100CX)
文摘The absorption coefficient of water is an important bio-optical parameter for water optics and water color remote sensing. However, scattering correction is essential to obtain accurate absorption coefficient values in situ using the nine-wavelength absorption and attenuation meter AC9. Establishing the correction always fails in Case 2 water when the correction assumes zero absorption in the near-infrared(NIR) region and underestimates the absorption coefficient in the red region, which affect processes such as semi-analytical remote sensing inversion. In this study, the scattering contribution was evaluated by an exponential fitting approach using AC9 measurements at seven wavelengths(412, 440, 488, 510, 532, 555, and 715 nm) and by applying scattering correction. The correction was applied to representative in situ data of moderately turbid coastal water, highly turbid coastal water, eutrophic inland water, and turbid inland water. The results suggest that the absorption levels in the red and NIR regions are significantly higher than those obtained using standard scattering error correction procedures. Knowledge of the deviation between this method and the commonly used scattering correction methods will facilitate the evaluation of the effect on satellite remote sensing of water constituents and general optical research using different scatteringcorrection methods.
文摘This study proposes a three-dimensional(3D)coupled magneto-electro-elastic problem for the static analysis of multilayered plates embedding piezomagnetic and piezoelectric layers by considering both sensor and actuator configurations.The 3D governing equations for the magneto-electro-elastic static behavior of plates are explicitly show that are made by the three 3D equilibrium equations,the 3D divergence equation for magnetic induction,and the 3D divergence equation for the electric displacement.The proposed solution involves the exponential matrix in the thickness direction and primary variables’harmonic forms in the in-plane ones.A closed-form solution is performed considering simply-supported boundary conditions.Interlaminar continuity conditions are imposed for displacements,magnetic potential,electric potential,transverse shear/normal stresses,transverse normal magnetic induction and transverse normal electric displacement.Therefore,a layerwise approach is adopted.The results section is composed of an assessment part,where the present model is compared to past 3D electro-elastic or magneto-elastic formulations and a new benchmark part.Benchmarks consider sensor and actuator plate configurations for the fully coupled magneto-electro-elastic cases for different thickness ratios.Tabular and graphical results are presented for displacements,stresses,magnetic potential,electric potential,transverse normal magnetic induction and transverse normal electric displacement.For each presented benchmark,magneto-electro-elastic coupling and thickness and material layer effects are discussed in depth.
基金Supported by NSFC(Grant No.12071419)the Natural Science Foundation of Shandong Province,China(Grant No.ZR2024MA056)。
文摘In this paper,we formulate two new families of fourth-order explicit exponential Runge–Kutta(ERK)methods with four stages for solving first-order differential systems y'(t)+M y(t)=f(y(t)).The order conditions of these ERK methods are derived by comparing the Taylor series of the exact solution,which are exactly identical to the order conditions of explicit Runge–Kutta methods,and these ERK methods reduce to classical Runge–Kutta methods once M→0.Moreover,we analyze the stability properties and the convergence of these new methods.Several numerical examples are implemented to illustrate the accuracy and efficiency of these ERK methods by comparison with standard exponential integrators.
文摘A three-dimensional(3D)analytical formulation is proposed to put together magnetic,electric and elastic fields to analyze the vibration modes of simply-supported layered piezo-electro-magnetic plates.The present 3D model allows analyses for layered smart plates in both open-circuit and closed-circuit configurations.The secondorder differential equations written in the mixed curvilinear reference system govern the magneto-electro-elastic free vibration problem for multilayered plates.This set consists of the 3D equations of motion and the 3D divergence equations for the magnetic induction and electric displacement.Navier harmonic forms in the planar directions and the exponential matrix method in the transversal direction of the plate are applied to solve the second-order differential equations in terms of displacements.For these reasons,simply-supported boundary conditions are considered.Imposition of interlaminar continuity conditions on primary variables(displacements,magnetic potential,electric potential),and some secondary variables(transverse normal and transverse shear stresses,transverse normal magnetic induction/electric displacement)allows the implementation of the layer-wise approach.Assessments for both load boundary configurations are proposed in the results section to validate the present 3D approach.3D electro-elastic and 3D magneto-elastic coupling validations are performed separately considering different models from the open literature.A new benchmark involving a full magneto-electro-elastic coupling for multilayered plates is presented considering both load boundary configurations for different thickness ratios.For this benchmark,circular frequency values and related vibration modes through the transverse direction in terms of displacements,magnetic and electric potential,transverse normal magnetic induction/electric displacement are shown to visualize the magneto-electroelastic coupling and material and thickness layer effects.The present formulation has been entirely implemented in an academic Matlab(R2024a)code developed by the authors.In this paper,for the first time,the second-order differential equations governing the magneto-electro-elastic problem for the free vibration analysis of plates has been solved considering the mixed mode of harmonic forms and exponential matrix.The exponential matrix permits computing the secondary variable of the problem(stresses,electric displacement components and magnetic induction components)exactly,directly from constitutive and geometrical equations.In addition,the very simple and elegant formulation permits having a code with very low computational costs.The present manuscript aims to fill the void in open literature regarding reference 3D solutions for the free vibration analysis of magneto-electro-elastic plates.
基金supported by Junta de Castilla y León and Feder(Project VA169P20).
文摘In a previous paper,a technique was suggested to avoid order reduction with any explicit exponential Runge-Kutta method when integrating initial boundary value nonlinear problems with time-dependent boundary conditions.In this paper,we significantly simplify the full discretization formulas to be applied under conditions which are nearly always satisfied in practice.Not only a simpler linear combination of'j-functions is given for both the stages and the solution,but also the information required on the boundary is so much simplified that,in order to get local order three,it is no longer necessary to resort to numerical differentiation in space.In many cases,even to get local order 4.The technique is then shown to be computationally competitive against other widely used methods with high enough stiff order through the standard method of lines.
基金supported by National Natural Science Foundation of China(Grant No.12371409)supported by National Natural Science Foundation of China(Grant No.12271240)+1 种基金National Natural Science Foundation of China/Hong Kong Research Grants Council Joint Research Scheme(Grant No.11961160718)the Shenzhen Natural Science Fund(Grant No.RCJC20210609103819018)。
文摘In this paper,we develop a general framework for constructing higher-order,unconditionally energydecreasing exponential time differencing Runge-Kutta(ETDRK)methods applicable to a range of gradient flows.Specifically,we identify conditions sufficient for ETDRK schemes to maintain the original energy dissipation.Our analysis reveals that the widely-employed third-and fourth-order ETDRK schemes fail to meet these conditions.To address this,we introduce new third-order ETDRK schemes,designed with appropriate stabilization,which satisfy these conditions and thus guarantee the unconditional energy decay property.We conduct extensive numerical experiments with these new schemes to verify their accuracy,stability,behavior under large time steps,long-term evolution,and adaptive time-stepping strategy across various gradient flows.This study offers the first framework to examine the unconditional energy stability of high-order ETDRK methods,and we are optimistic that our framework will enable the development of ETDRK schemes beyond the third order that are unconditionally energy stable.
文摘The present paper deals with the Sharma-Tasso-Olver-Burgers equation(STOBE)and its conservation laws and kink solitons.More precisely,the formal Lagrangian,Lie symmetries,and adjoint equations of the STOBE are firstly constructed to retrieve its conservation laws.Kink solitons of the STOBE are then extracted through adopting a series of newly well-designed approaches such as Kudryashov and exponential methods.Diverse graphs in 2 and 3D postures are formally portrayed to reveal the dynamical features of kink solitons.According to the authors’knowledge,the outcomes of the current investigation are new and have been listed for the first time.
基金supported by National Natural Science Foundation of China(11961002,11761007,11861007)Key Project of the Natural Science Foundation of Jiangxi Province(20212ACB201001).
文摘In this paper,we mainly study an inverse source problem of time fractional diffusion equation in a bounded domain with an over-specified terminal condition at a fixed time.A novel regularization method,which we call the exponential Tikhonov regularization method with a parameter γ,is proposed to solve the inverse source problem,and the corresponding convergence analysis is given under a-priori and a-posteriori regularization parameter choice rules.Whenγis less than or equal to zero,the optimal convergence rate can be achieved and it is independent of the value of γ.However,when γ is greater than zero,the optimal convergence rate depends on the value of γ which is related to the regularity of the unknown source.Finally,numerical experiments are conducted for showing the effectiveness of the proposed exponential regularization method.
基金funded by the Science and Engineering Research Board,SERB-DST,India,under project scheme MATRICS(MTR/2020/000531)。
文摘The prime objective of this paper is to explore the new exact soliton solutions to the higher-dimensional nonlinear Fokas equation and(2+1)-dimensional breaking soliton equations via a generalized exponential rational function(GERF) method. Many different kinds of exact soliton solution are obtained, all of which are completely novel and have never been reported in the literature before. The dynamical behaviors of some obtained exact soliton solutions are also demonstrated by a choice of appropriate values of the free constants that aid in understanding the nonlinear complex phenomena of such equations. These exact soliton solutions are observed in the shapes of different dynamical structures of localized solitary wave solutions, singular-form solitons, single solitons,double solitons, triple solitons, bell-shaped solitons, combo singular solitons, breather-type solitons,elastic interactions between triple solitons and kink waves, and elastic interactions between diverse solitons and kink waves. Because of the reduction in symbolic computation work and the additional constructed closed-form solutions, it is observed that the suggested technique is effective, robust, and straightforward. Moreover, several other types of higher-dimensional nonlinear evolution equation can be solved using the powerful GERF technique.
文摘In this paper, a novel class of exponential Fourier collocation methods （EFCMs） is presented for solving systems of first-order ordinary differential equations. These so-called exponential Fourier collocation methods are based on the variation-of-constants formula, incorporating a local Fourier expansion of the underlying problem with collocation meth- ods. We discuss in detail the connections of EFCMs with trigonometric Fourier colloca- tion methods （TFCMs）, the well-known Hamiltonian Boundary Value Methods （HBVMs）, Gauss methods and Radau IIA methods. It turns out that the novel EFCMs are an es- sential extension of these existing methods. We also analyse the accuracy in preserving the quadratic invariants and the Hamiltonian energy when the underlying system is a Hamiltonian system. Other properties of EFCMs including the order of approximations and the convergence of fixed-point iterations are investigated as well. The analysis given in this paper proves further that EFCMs can achieve arbitrarily high order in a routine manner which allows us to construct higher-order methods for solving systems of first- order ordinary differential equations conveniently. We also derive a practical fourth-order EFCM denoted by EFCM（2,2） as an illustrative example. The numerical experiments using EFCM（2,2） are implemented in comparison with an existing fourth-order HBVM, an energy-preserving collocation method and a fourth-order exponential integrator in the literature. The numerical results demonstrate the remarkable efficiency and robustness of the novel EFCM（2,2）.
基金supported by the NSF grant DMS-1114546 and NSF Research Network in Mathematical Sciences“KI-Net:Kinetic description of emerging challenges in multiscale problems of natural sciences”X.Y.was partially supported by the startup funding of University of California,Santa Barbara。
文摘This paper generalizes the exponential Runge-Kutta asymptotic preserving(AP)method developed in[G.Dimarco and L.Pareschi,SIAM Numer.Anal.,49(2011),pp.2057–2077]to compute the multi-species Boltzmann equation.Compared to the single species Boltzmann equation that the method was originally applied on,this set of equation presents a new difficulty that comes from the lack of local conservation laws due to the interaction between different species.Hence extra stiff nonlinear source terms need to be treated properly to maintain the accuracy and the AP property.The method we propose does not contain any nonlinear nonlocal implicit solver,and can capture the hydrodynamic limit with time step and mesh size independent of the Knudsen number.We prove the positivity and strong AP properties of the scheme,which are verified by two numerical examples.
文摘Throughput prediction is essential for congestion control and LTE network management. In this paper, the autoregressive integrated moving average （ARIMA） model and exponential smoothing model are used to predict the throughput in a single cell and whole region in an LTE network. The experimental results show that these two models perform differently in both scenarios. The ARIMA model is better than the exponential smoothing model for predicting throughput on weekdays in a whole region. The exponential smoothing model is better than the ARIMA model for predicting throughput on weekends in a whole region. The exponential smoothing model is better than the ARIMA model for predicting throughput in a single cell. In these two LTE network scenarios, throughput prediction based on traffic time series leads to more efficient resource management and better QoS.
文摘An efficient and accurate exponential wave integrator Fourier pseudospectral （EWI-FP） method is proposed and analyzed for solving the symmetric regularized-long-wave （SRLW） equation, which is used for modeling the weakly nonlinear ion acoustic and space-charge waves. The numerical method here is based on a Gautschi-type exponential wave integrator for temporal approximation and the Fourier pseudospectral method for spatial discretization. The scheme is fully explicit and efficient due to the fast Fourier transform. Numerical analysis of the proposed EWI-FP method is carried out and rigorous error estimates are established without CFL-type condition by means of the mathematical induction. The error bound shows that EWI-FP has second order accuracy in time and spectral accuracy in space. Numerical results are reported to confirm the theoretical studies and indicate that the error bound here is optimal.
基金This study was supported by the Major State Basic Research Program of China under contract No.G2000078503the National Natural Science Foundation of China under contract No.40246024.
文摘Research on heat and mass flux yielded by modern seafloor hydrothermal activity is very important, because it is involved not only in the base of ocean environment research, but also in the historical evolution of seawater properties. Currently, estimating heat flux is based on the observation data of hydrothermal smokers, low-temperature diffusive flow and mid-ocean ridge mainly. But there are some faults, for example, there is lack of a concurrent conductive item in estimating the heat flux by smokers and the error between the half-space cooling model and the observation data is too large. So, three kinds of methods are applied to re-estimating the heat flux of hydrothermal activity resepectively, corresponding estimation is 97. 359 GW by hydrothermal smoker and diffusive flow, 84.895 GW by hydrothermal plume, and 4. 11 TW by exponential attenuation method put forward by this paper. Research on mass flux estimation is relatively rare, the main reason for this is insufficient field observation data. Mass fluxes of different elements are calculated using hydrothermal vent fluid data from the TAG hydrothermal area on the Mid-Atlantic Ridge for the first time. Difference of estimations by different methods reflects the researching extent of hydrothermal activity, and systematically in - situ observation will help to estimate the contribution of hydrothermal activity to ocean chemical environment, ocean circulation and global climate precisely.
