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A Hybrid ESA-CCD Method for Variable-Order Time-Fractional Diffusion Equations
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作者 Xiaoxue Lu Chunhua Zhang +1 位作者 Huiling Xue Bowen Zhong 《Journal of Applied Mathematics and Physics》 2024年第9期3053-3065,共13页
In this paper, we study the solutions for variable-order time-fractional diffusion equations. A three-point combined compact difference (CCD) method is used to discretize the spatial variables to achieve sixth-order a... In this paper, we study the solutions for variable-order time-fractional diffusion equations. A three-point combined compact difference (CCD) method is used to discretize the spatial variables to achieve sixth-order accuracy, while the exponential-sum-approximation (ESA) is used to approximate the variable-order Caputo fractional derivative in the temporal direction, and a novel spatial sixth-order hybrid ESA-CCD method is implemented successfully. Finally, the accuracy of the proposed method is verified by numerical experiments. 展开更多
关键词 Variable-Order Caputo Fractional Derivative Combined Compact Difference Method Exponential-Sum-Approximation
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Compact implicit integration factor methods for some complex-valued nonlinear equations 被引量:1
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作者 张荣培 《Chinese Physics B》 SCIE EI CAS CSCD 2012年第4期49-53,共5页
The compact implicit integration factor (cIIF) method is an efficient time discretization scheme for stiff nonlinear diffusion equations in two and three spatial dimensions. In the current work, we apply the cIIF me... The compact implicit integration factor (cIIF) method is an efficient time discretization scheme for stiff nonlinear diffusion equations in two and three spatial dimensions. In the current work, we apply the cIIF method to some complex-valued nonlinear evolutionary equations such as the nonlinear SchrSdinger (NLS) equation and the complex Ginzburg-Landau (GL) equation. Detailed algorithm formulation and practical implementation of cIIF method are performed. The numerical results indicate that this method is very accurate and efficient. 展开更多
关键词 compact implicit integration factor method finite difference nonlinear Schrodinger equa-tion complex Ginzburg Landau equation
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New Method of Total Ionizing Dose Compact Modeling in Partially Depleted Silicon-on-Insulator MOSFETs 被引量:4
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作者 黄建强 何伟伟 +3 位作者 陈静 罗杰馨 吕凯 柴展 《Chinese Physics Letters》 SCIE CAS CSCD 2016年第9期82-85,共4页
On the basis of a detailed discussion of the development of total ionizing dose (TID) effect model, a new commercial-model-independent TID modeling approach for partially depleted silicon-on-insulator metal-oxide- s... On the basis of a detailed discussion of the development of total ionizing dose (TID) effect model, a new commercial-model-independent TID modeling approach for partially depleted silicon-on-insulator metal-oxide- semiconductor field effect transistors is developed. An exponential approximation is proposed to simplify the trap charge calculation. Irradiation experiments with 60Co gamma rays for IO and core devices are performed to validate the simulation results. An excellent agreement of measurement with the simulation results is observed. 展开更多
关键词 of New Method of Total Ionizing Dose Compact Modeling in Partially Depleted Silicon-on-Insulator MOSFETs for SOI TID in is IO NMOS on
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HLDER ESTIMATES FOR A CLASS OF DEGENERATE ELLIPTIC EQUATIONS 被引量:1
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作者 宋巧珍 王立河 李东升 《Acta Mathematica Scientia》 SCIE CSCD 2013年第4期1202-1218,共17页
In this paper we study the regularity theory of the solutions of a class of degenerate elliptic equations in divergence form. By introducing a proper distance and applying the compactness method we establish the HSlde... In this paper we study the regularity theory of the solutions of a class of degenerate elliptic equations in divergence form. By introducing a proper distance and applying the compactness method we establish the HSlder type estimates for the weak solutions. 展开更多
关键词 degenerate elliptic equations HSlder estimates compactness method
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A Multi-Symplectic Compact Method for the Two-Component Camassa-Holm Equation with Singular Solutions
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作者 Xiang Li Xu Qian +1 位作者 Bo-Ya Zhang Song-He Song 《Chinese Physics Letters》 SCIE CAS CSCD 2017年第9期8-12,共5页
The two-component Camassa–Holm equation includes many intriguing phenomena. We propose a multi-symplectic compact method to solve the two-component Camassa–Holm equation. Based on its multi-symplectic formulation, t... The two-component Camassa–Holm equation includes many intriguing phenomena. We propose a multi-symplectic compact method to solve the two-component Camassa–Holm equation. Based on its multi-symplectic formulation, the proposed method is derived by the sixth-order compact finite difference method in spatial discretization and the symplectic implicit midpoint scheme in temporal discretization. Numerical experiments finely describe the velocity and density variables in the two-component integrable system and distinctly display the evolvement of the singular solutions. Moreover, the proposed method shows good conservative properties during long-time numerical simulation. 展开更多
关键词 A Multi-Symplectic Compact Method for the Two-Component Camassa-Holm Equation with Singular Solutions
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A Compact Difference Method for Viscoelastic Plate Vibration Equation
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作者 Cailian Wu Congcong Wei Ailing Zhu 《Engineering(科研)》 2021年第11期631-645,共15页
In this paper, a fourth-order viscoelastic plate vibration equation is transformed into a set of two second-order differential equations by introducing an intermediate variable. A three-layer compact difference scheme... In this paper, a fourth-order viscoelastic plate vibration equation is transformed into a set of two second-order differential equations by introducing an intermediate variable. A three-layer compact difference scheme for the initial-boundary value problem of the viscoelastic plate vibration equation is established. Then the stability and convergence of the difference scheme are analyzed by the energy method, and the convergence order is <img src="Edit_0a250b60-7c3c-4caf-8013-5e302d6477ab.png" alt="" />. Finally, some numerical examples are given of which results verify the accuracy and validity of the scheme. 展开更多
关键词 Viscoelastic Plate Vibration Equation Compact Difference Method STABILITY CONVERGENCE
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Computational Studies of Reaction-Diffusion Systems by Nonlinear Galerkin Method
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作者 Miroslav Kolar 《American Journal of Computational Mathematics》 2013年第2期137-146,共10页
This article deals with the computational study of the nonlinear Galerkin method, which is the extension of commonly known Faedo-Galerkin method. The weak formulation of the method is derived and applied to the partic... This article deals with the computational study of the nonlinear Galerkin method, which is the extension of commonly known Faedo-Galerkin method. The weak formulation of the method is derived and applied to the particular Scott-Wang-Showalter reaction-diffusion model concerning the problem of combustion of hydrocarbon gases. The proof of convergence of the method based on the method of compactness is introduced. Presented results of numerical simulations are composed of the computational study, where the nonlinear Galerkin method and Faedo-Galerkin method are compared for the problem with analytical solution and the numerical results of the Scott-Wang-Showalter model in 1D. 展开更多
关键词 Nonlinear Galerkin Method Scott-Wang-Showalter Model Compactness Method
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UNIFORM ERROR BOUNDS OF A CONSERVATIVE COMPACT FINITE DIFFERENCE METHOD FOR THE QUANTUM ZAKHAROV SYSTEM IN THE SUBSONIC LIMIT REGIME
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作者 Gengen Zhang Chunmei Su 《Journal of Computational Mathematics》 SCIE CSCD 2024年第1期289-312,共24页
In this paper,we consider a uniformly accurate compact finite difference method to solve the quantum Zakharov system(QZS)with a dimensionless parameter 0<ε≤1,which is inversely proportional to the acoustic speed.... In this paper,we consider a uniformly accurate compact finite difference method to solve the quantum Zakharov system(QZS)with a dimensionless parameter 0<ε≤1,which is inversely proportional to the acoustic speed.In the subsonic limit regime,i.e.,when 0<ε?1,the solution of QZS propagates rapidly oscillatory initial layers in time,and this brings significant difficulties in devising numerical algorithm and establishing their error estimates,especially as 0<ε?1.The solvability,the mass and energy conservation laws of the scheme are also discussed.Based on the cut-off technique and energy method,we rigorously analyze two independent error estimates for the well-prepared and ill-prepared initial data,respectively,which are uniform in both time and space forε∈(0,1]and optimal at the fourth order in space.Numerical results are reported to verify the error behavior. 展开更多
关键词 Quantum Zakharov system Subsonic limit Compact finite difference method Uniformly accurate Error estimate
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New Numerical Methods for the Coupled Nonlinear Schrdinger Equations 被引量:1
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作者 Qiu-bin Xu Qian-shun Chang 《Acta Mathematicae Applicatae Sinica》 SCIE CSCD 2010年第2期205-218,共14页
In this paper, three numerical schemes with high accuracy for the coupled Schrodinger equations are studied. The conserwtive properties of the schemes are obtained and the plane wave solution is analysised. The split ... In this paper, three numerical schemes with high accuracy for the coupled Schrodinger equations are studied. The conserwtive properties of the schemes are obtained and the plane wave solution is analysised. The split step Runge-Kutta scheme is conditionally stable by linearized analyzed. The split step compact scheme and the split step spectral method are unconditionally stable. The trunction error of the schemes are discussed. The fusion of two solitions colliding with different β is shown in the figures. The numerical experments demonstrate that our algorithms are effective and reliable. 展开更多
关键词 Coupled nonlinear Schrodinger equation(CNLS) split step Runge-Kutta method compact scheme split step spectral method difference scheme
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A robust compact least-squares reconstruction method for compressible turbulent flow simulations of complex configurations
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作者 Jia YAN Zhengyu NIU +3 位作者 Xiaoquan YANG Jue DING Xiaolong TANG Peifeng WENG 《Chinese Journal of Aeronautics》 SCIE EI CAS CSCD 2023年第12期113-138,共26页
For the second-order finite volume method,implicit schemes and reconstruction methods are two main algorithms which influence the robustness and efficiency of the numerical simulations of compressible turbulent flows.... For the second-order finite volume method,implicit schemes and reconstruction methods are two main algorithms which influence the robustness and efficiency of the numerical simulations of compressible turbulent flows.In this paper,a compact least-squares reconstruction method is proposed to calculate the gradients for the distribution of flow field variables approximation.The compactness of the new reconstruction method is reflected in the gradient calculation process.The geometries of the face-neighboring elements are no longer utilized,and the weighted average values at the centroid of the interfaces are used to calculate the gradients instead of the values at the centroid of the face-neighboring elements.Meanwhile,an exact Jacobian solving strategy is developed for implicit temporal discretization.The accurate processing of Jacobian matrix can extensively improve the invertibility of the Jacobian matrix and avoid introducing extra numerical errors.In addition,a modified Venkatakrishnan limiter is applied to deal with the shock which may appear in transonic flows and the applicability of the mentioned methods is enhanced further.The combination of the proposed methods makes the numerical simulations of turbulent flow converge rapidly and steadily with an adaptive increasing CFL number.The numerical results of several benchmarks indicate that the proposed methods perform well in terms of robustness,efficiency and accuracy,and have good application potential in turbulent flow simulations of complex configurations. 展开更多
关键词 Compact least-squares reconstruction method Exact Jacobian matrix Finite volume method Implicit schemes Turbulent flow
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HIGH ORDER COMPACT MULTISYMPLECTIC SCHEME FOR COUPLED NONLINEAR SCHRODINGER-KDV EQUATIONS 被引量:1
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作者 Lan Wang Yushun Wang 《Journal of Computational Mathematics》 SCIE CSCD 2018年第4期591-604,共14页
In this paper, a novel multisymplectic scheme is proposed for the coupled nonlinear Schrodinger-KdV (CNLS-KdV) equations. The CNLS-KdV equations are rewritten into the multisymplectic Hamiltonian form by introducing... In this paper, a novel multisymplectic scheme is proposed for the coupled nonlinear Schrodinger-KdV (CNLS-KdV) equations. The CNLS-KdV equations are rewritten into the multisymplectic Hamiltonian form by introducing some canonical momenta. To simulate the problem efficiently, the CNLS-KdV equations are approximated by a high order compact method in space which preserves N semi-discrete multisymplectic conservation laws. We then discretize the semi-discrete system by using a symplectic midpoint scheme in time. Thus, a full-discrete multisymplectic scheme is obtained for the CNLS-KdV equations. The conservation laws of the full-discrete scheme are analyzed. Some numerical experiments are presented to further verify the convergence and conservation laws of the new scheme. 展开更多
关键词 Schrodinger-KdV equations High order compact method Conservation law Multisymplectic scheme
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High order sub-cell finite volume schemes for solving hyperbolic conservation laws I: basic formulation and one-dimensional analysis 被引量:1
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作者 JianHua Pan YuXin Ren 《Science China(Physics,Mechanics & Astronomy)》 SCIE EI CAS CSCD 2017年第8期60-75,共16页
In this paper, a family of sub-cell finite volume schemes for solving the hyperbolic conservation laws is proposed and analyzed in one-dimensional cases. The basic idea of this method is to subdivide a control volume(... In this paper, a family of sub-cell finite volume schemes for solving the hyperbolic conservation laws is proposed and analyzed in one-dimensional cases. The basic idea of this method is to subdivide a control volume(main cell) into several sub-cells and the finite volume discretization is applied to each of the sub-cells. The averaged values on the sub-cells of current and face neighboring main cells are used to reconstruct the polynomial distributions of the dependent variables. This method can achieve arbitrarily high order of accuracy using a compact stencil. It is similar to the spectral volume method incorporating with PNPM technique but with fundamental differences. An elaborate utilization of these differences overcomes some shortcomings of the spectral volume method and results in a family of accurate and robust schemes for solving the hyperbolic conservation laws. In this paper, the basic formulation of the proposed method is presented. The Fourier analysis is performed to study the properties of the one-dimensional schemes. A WENO limiter based on the secondary reconstruction is constructed. 展开更多
关键词 compact high order method sub-cell finite volume method unstructured grid
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Optimal Error Estimates of Compact Finite Difference Discretizations for the Schrodinger-Poisson System 被引量:1
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作者 Yong Zhang 《Communications in Computational Physics》 SCIE 2013年第5期1357-1388,共32页
We study compact finite difference methods for the Schrodinger-Poisson equation in a bounded domain and establish their optimal error estimates under proper regularity assumptions on wave functionψand external potent... We study compact finite difference methods for the Schrodinger-Poisson equation in a bounded domain and establish their optimal error estimates under proper regularity assumptions on wave functionψand external potential V(x).The CrankNicolson compact finite difference method and the semi-implicit compact finite difference method are both of order O(h^(4)+τ^(2))in discrete l^(2),H^(1) and l^(∞) norms with mesh size h and time step τ.For the errors of compact finite difference approximation to the second derivative and Poisson potential are nonlocal,thus besides the standard energy method and mathematical induction method,the key technique in analysis is to estimate the nonlocal approximation errors in discrete l^(∞) and H^(1) norm by discrete maximum principle of elliptic equation and properties of some related matrix.Also some useful inequalities are established in this paper.Finally,extensive numerical results are reported to support our error estimates of the numerical methods. 展开更多
关键词 Schrodinger-Poisson system Crank-Nicolson scheme semi-implicit scheme compact finite difference method Gronwall inequality the maximum principle
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An exponential expanding meshes sequence and finite difference method adopted for two-dimensional elliptic equations
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作者 Navnit Jha Neelesh Kumar 《International Journal of Modeling, Simulation, and Scientific Computing》 EI 2016年第2期109-125,共17页
We demonstrate a new nonuniform mesh finite difference method to obtain accurate solutions for the elliptic partial differential equations in two dimensions with nonlinear first-order partial derivative terms.The meth... We demonstrate a new nonuniform mesh finite difference method to obtain accurate solutions for the elliptic partial differential equations in two dimensions with nonlinear first-order partial derivative terms.The method will be based on a geometric grid network area and included among the most stable differencing scheme in which the nine-point spatial finite differences are implemented,thus arriving at a compact formulation.In general,a third order of accuracy has been achieved and a fourth-order truncation error in the solution values will follow as a particular case.The efficiency of using geometric mesh ratio parameter has been shown with the help of illustrations.The convergence of the scheme has been established using the matrix analysis,and irreducibility is proved with the help of strongly connected characteristics of the iteration matrix.The difference scheme has been applied to test convection diffusion equation,steady state Burger’s equation,ocean model and a semi-linear elliptic equation.The computational results confirm the theoretical order and accuracy of the method. 展开更多
关键词 Geometric mesh finite difference compact method elliptic partial differential equations convection diffusion equation Stommel ocean model
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A HIGH-ORDER FINITE DIFFERENCE METHOD FOR UNSTEADY CONVECTION-DIFFUSION PROBLEMS WITH SOURCE TERM
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作者 Yang Zhi-feng Wang Xuan(State Key Laboratory of Environment Simulation and Pollution Control, Institute of Environmental Sciences, Beijing Normal University, Beijing 100875, P. R. China.) 《Journal of Hydrodynamics》 SCIE EI CSCD 1999年第2期97-102,共6页
The convection and diffusion are the basic processes in fluid flow and heat& mass transfer. The upwind and evolution functions for the convection term are introduced to give a comprehensive transformation to one-d... The convection and diffusion are the basic processes in fluid flow and heat& mass transfer. The upwind and evolution functions for the convection term are introduced to give a comprehensive transformation to one-dimensional unsteady convection-diffusion equation involving source term. The corresponding compact fourth-order finite difference methed is developed. With the trans formation, the authors overcome the difficultyin dealing with the convection term, and the high-order expression for the convection-diffusion term can be conveniently obtained. The proposed difference scheme with thefourth-order accuracy and unconditional stability can fully reflect the upwind and evolutioneffects of the convection. The calculated results show that the errors of the referencescheme are 600 or 6000 times those of the proposed scheme for the same computationalgrid. With the one time decrease of the space grid, the errors of the proposed scheme andthe reference scheme reduce about 20 times and 2 times respectively. It is evident that theaccuracy of the proposed scheme is remarkably higher than that of the reference scheme. 展开更多
关键词 CONVECTION-DIFFUSION compact difference method comprehensive transformation UNSTEADY computational fluid dynamics
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A COMPACT FOURTH-ORDER FINITE DIFFERENCE SCHEME FOR THE IMPROVED BOUSSINESQ EQUATION WITH DAMPING TERMS
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作者 Fuqiang Lu Zhiyao Song Zhuo Zhang 《Journal of Computational Mathematics》 SCIE CSCD 2016年第5期462-478,共17页
In this paper, a compact finite difference method is presented for solving the initial boundary value problems for the improved Boussinesq equation with damping terms. The fourth-order equation can be transformed into... In this paper, a compact finite difference method is presented for solving the initial boundary value problems for the improved Boussinesq equation with damping terms. The fourth-order equation can be transformed into a first-order ordinary differential system, and then, the classical Pad4 approximation is used to discretize spatial derivative in the non- linear partial differential equations. The resulting coefficient matrix for the semi-discrete scheme is tri-diagonal and can be solved efficiently. In order to maintain the same order of convergence, the classical fourth-order Runge-Kutta method is the preferred method for explicit time integration. Soliton-type solutions are used to evaluate the accuracy of the method, and various numerical experiments are designed to test the different effects of the damping terms. 展开更多
关键词 Compact finite difference method hnproved Boussinesq equation Stokesdamping Hydrodynamic damping Runge-Kutta method.
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An Energy-Preserving Scheme for the Coupled Gross-Pitaevskii Equations
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作者 Lan Wang Wenjun Cai YushunWang 《Advances in Applied Mathematics and Mechanics》 SCIE 2021年第1期203-231,共29页
An energy-preserving scheme is proposed for the coupled Gross-Pitaevskii equations.The scheme is constructed by high order compact method in the spatial direction and average vector field method in the temporal direct... An energy-preserving scheme is proposed for the coupled Gross-Pitaevskii equations.The scheme is constructed by high order compact method in the spatial direction and average vector field method in the temporal direction,respectively.The scheme is energy-preserving,stable,and of sixth order in space and of second order in time.Numerical experiments verify the theoretical results.The dynamic behavior modeled by the coupled Gross-Pitaevskii equations is also numerically investigated. 展开更多
关键词 Coupled Gross-Pitaevskii equations average vector field method high order compact method energy-preserving scheme
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Compact splitting symplectic scheme for the fourth-order dispersive Schrodinger equation with Cubic-Quintic nonlinear term
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作者 Lang-Yang Huang Zhi-Feng Weng Chao-Ying Lin 《International Journal of Modeling, Simulation, and Scientific Computing》 EI 2019年第2期142-155,共14页
Combining symplectic algorithm,splitting technique and compact method,a compact splitting symplectic scheme is proposed to solve the fourth-order dispersive Schr¨odinger equation with cubic-quintic nonlinear term... Combining symplectic algorithm,splitting technique and compact method,a compact splitting symplectic scheme is proposed to solve the fourth-order dispersive Schr¨odinger equation with cubic-quintic nonlinear term.The scheme has fourth-order accuracy in space and second-order accuracy in time.The discrete charge conservation law and stability of the scheme are analyzed.Numerical examples are given to confirm the theoretical results. 展开更多
关键词 Symplectic scheme Schr¨odinger equation compact splitting method conservation law
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A conservative numerical method for the fractional nonlinear Schrodinger equation in two dimensions
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作者 Rongpei Zhang Yong-Tao Zhang +2 位作者 Zhen Wang Bo Chen Yi Zhang 《Science China Mathematics》 SCIE CSCD 2019年第10期1997-2014,共18页
This paper proposes and analyzes an efficient finite difference scheme for the two-dimensional nonlinear Schr?dinger(NLS) equation involving fractional Laplacian. The scheme is based on a weighted and shifted Grü... This paper proposes and analyzes an efficient finite difference scheme for the two-dimensional nonlinear Schr?dinger(NLS) equation involving fractional Laplacian. The scheme is based on a weighted and shifted Grünwald-Letnikov difference(WSGD) operator for the spatial fractional Laplacian. We prove that the proposed method preserves the mass and energy conservation laws in semi-discrete formulations. By introducing the differentiation matrices, the semi-discrete fractional nonlinear Schr?dinger(FNLS) equation can be rewritten as a system of nonlinear ordinary differential equations(ODEs) in matrix formulations. Two kinds of time discretization methods are proposed for the semi-discrete formulation. One is based on the Crank-Nicolson(CN) method which can be proved to preserve the fully discrete mass and energy conservation. The other one is the compact implicit integration factor(c IIF) method which demands much less computational effort. It can be shown that the cIIF scheme can approximate CN scheme with the error O(τ~2). Finally numerical results are presented to demonstrate the method’s conservation, accuracy, efficiency and the capability of capturing blow-up. 展开更多
关键词 fractional nonlinear Schrodinger equation weighted and shifted Grünwald-Letnikov difference compact integration factor method CONSERVATION
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ON THE HOMOGENIZATION OF DEGENERATE PARABOLIC EQUATIONS 被引量:10
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作者 简怀玉 《Acta Mathematicae Applicatae Sinica》 SCIE CSCD 2000年第1期100-110,共11页
The homogenization of the nonlinear degenerate parabolic equations, diva(x/ε,t/ε,u,u)=f(x,t) is studied, where a(y,t,μ,λ) is periodic in (y,t) and b may be a nonlinear function whose prototype is |μ|~r sign u wi... The homogenization of the nonlinear degenerate parabolic equations, diva(x/ε,t/ε,u,u)=f(x,t) is studied, where a(y,t,μ,λ) is periodic in (y,t) and b may be a nonlinear function whose prototype is |μ|~r sign u with r>0. 展开更多
关键词 Parabolic equation HOMOGENIZATION boundary value problem compactness method
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