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The Uniform L^2 Behavior for time discretization of an Evolution Equation

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Acta Mathematica Sinica,English Series 2003年第1期19卷 127-140页

作者： DaXU DepartmentofMathematics HunanNormalUniversityChangsha410081

The uniform L^2 stability and convergence properties for the time discretization of an evolution equation with a memory term are studied. The methods are based on the second-order backward difference methods. The memo... 详细信息

关键词： Evolution equation with memory time discretization Uniform L 2 behavior

TWO-STAGE FOURTH-ORDER ACCURATE time discretizationS FOR 1D AND 2D SPECIAL RELATIVISTIC HYDRODYNAMICS

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Journal of Computational Mathematics 2020年第5期38卷 768-796页

作者： Yuhuan Yuan Huazhong Tang Center for Applied Physics and Technology HEDPSand LMAMSchool of Mathematical SciencesPeking UniversityBeijing 100871China

This paper studies the two-stage fourth-order accurate time discretization[*** and ***,SIAM ***.,38(2016)]and its application to the special relativistic hydrodynamical *** analysis reveals that the new two-stage fourth-order accurate time discretizations can be *** the aid of the direct Eulerian GRP(generalized Riemann problem)methods and the analytical resolution of the local“quasi 1D”GRP,the two-stage fourth-order accurate time discretizations are successfully implemented for the 1D and 2D special relativistic hydrodynamical *** numerical experiments demonstrate the performance and accuracy as well as robustness of our schemes.

关键词： time discretization Shock-capturing scheme GRP method Relativistic hydrodynamics Hyperbolic conservation laws

Approximating Stationary Statistical Properties

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Chinese Annals of Mathematics,Series B 2009年第6期30卷 831-844页

作者： Xiaoming WANG Dedicated to Professor Andrew Majda on the Occasion of his 60th Birthday with Admiration and Friendship）

It is well-known that physical laws for large chaotic dynamical systems are revealed *** times these statistical properties of the system must be approximated *** main contribution of this manuscript is to provide simple and natural criterions on numerical methods (temporal and spatial discretization) that are able to capture the stationary statistical properties of the underlying dissipative chaotic dynamical systems *** result on temporal approximation is a recent finding of the author,and the result on spatial approximation is a new *** to the infinite Prandtl number model for convection and the barotropic quasi-geostrophic model are also discussed.

关键词： Stationary statistical property Invariant measure Global attractor Dissipative system time discretization Spatial discretisation Uniformly dissipative scheme Infinite Prandtl number model for convection Barotropic quasi-geostrophic equations

Euler-type schemes for weakly coupled forward-backward stochastic differential equations and optimal convergence analysis

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Frontiers of Mathematics in China 2015年第2期10卷 415-434页

作者： Wei ZHANG Weidong ZHAO School of Mathematics Finance Institute Shandong University Jinan 250100 China

We introduce a new Euler-type scheme and its iterative algorithm for solving weakly coupled forward-backward stochastic differential equations （FBSDEs）. Although the schemes share some common features with the ones proposed by C. Bender and J. Zhang [Ann. Appl. Probab., 2008, 18： 143-177], less computational work is needed for our method. For both our schemes and the ones proposed by Bender and Zhang, we rigorously obtain first-order error estimates, which improve the half-order error estimates of Bender and Zhang. Moreover, numerical tests are given to demonstrate the first-order accuracy of the schemes.

关键词： Weakly coupled forward-backward stochastic differential equations (FBSDEs) Euler-type scheme time discretization first-order error estimate

A NOTE ON PRESSURE APPROXIMATION OF FIRST AND HIGHER ORDER PROJECTION SCHEMES FOR THE NONSTATIONARY INCOMPRESSIBLE NAVIER-STOKES EQUATIONS

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Journal of Computational Mathematics 2009年第2期27卷 338-347页

作者： Erich Carelli Andrcas Prohl Mathematisches Institut Universitt TübingenAuf der Morgenstelle 10D-72076 Tübingen

Projection methods are efficient operator-splitting schemes to approximate solutions of the incompressible Navier-Stokes equations. As a major drawback, they introduce spurious layers, both in space and time. In this work, we survey convergence results for higher order projection methods, in the presence of only strong solutions of the limiting problem; in particular, we highlight concomitant difficulties in the construction process of accurate higher order schemes, such as limited regularities of the limiting solution, and a lack of accurate initial data for the pressure. Computational experiments are included to compare the presented schemes, and illustrate the difficulties mentioned.

关键词： Incompressible Navier-Stokes equation time discretization Projection method

Local Discontinuous Galerkin Methods for High-Order time-Dependent Partial Differential Equations

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Communications in Computational Physics 2010年第1期7卷 1-46页

作者： Yan Xu Chi-Wang Shu Department of Mathematics University of Science and Technology of ChinaHefeiAnhui 230026China Division of Applied Mathematics Brown UniversityProvidenceRI 02912USA

Discontinuous Galerkin (DG) methods are a class of finite element methodsusing discontinuous basis functions, which are usually chosen as piecewise polynomi-als. Since the basis functions can be discontinuous, these methods have the flexibilitywhich is not shared by typical finite element methods, such as the allowance of ar-bitrary triangulation with hanging nodes, less restriction in changing the polynomialdegrees in each element independent of that in the neighbors (p adaptivity), and localdata structure and the resulting high parallel efficiency. In this paper, we give a generalreview of the local DG (LDG) methods for solving high-order time-dependent partialdifferential equations (PDEs). The important ingredient of the design of LDG schemes,namely the adequate choice of numerical fluxes, is highlighted. Some of the applica-tions of the LDG methods for high-order time-dependent PDEs are also be discussed.

关键词： Discontinuous Galerkin method local discontinuous Galerkin method numerical flux stability time discretization high order accuracy stability error estimates

MATHEMATICAL PROBLEMS ON THE FLUID-SOLUTE-HEAT FLOW THROUGH POROUS MEDIA Ⅱ. PARTIALLY SATURATED CASE

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Acta Mathematicae Applicatae Sinica 1990年第2期6卷 145-157页

作者：苏宁 Tsinghua University degenerate parabolic system arising from the fluid-solute-heat flow through partiallysaturated porous media is considered. The existence of weak solutions to the initial boundary valueproblem of this system is established by time discretization and the continuity of the weak solutionsis discussed.

A degenerate parabolic system arising from the fluid-solute-heat flow through partiallysaturated porous media is considered. The existence of weak solutions to the initial boundary valueproblem of this system is estab... 详细信息

关键词： Porous Medium Weak Solution time discretization Mathematical Problem Initial Boundary

KINETIC MODELLING AND PERFORMANCE ANALYSIS OF THE FOUR-POST-FRAME LIFTING MECHANICAL SYSTEM

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Journal of Shanghai Jiaotong university(Science) 2001年第2期6卷 191-196页

作者：高建华杨汝清胡洪国 Research Inst. of Robotics Shanghai Jiaotong Univ.

The kinetic model of the four-post-frame lifting mechanical system was established. The stiffness and damping matrices of differential equations of motion were obtained by using Lagrange’s equations. And the dynamic characteristics of system were analyzed by modal analysis method. Based upon this, the modifications of structural parameters which can improve dynamic performance were discussed. The low-level high-speed palletizer MDJ1200L was taken as a real case in the paper.

关键词： lifting mechanical system modal analysis method time discretization dynamic characteristic

New approach to robust stabilization for a class of singular systems with time-delays

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New approach to robust stabilization for a class of singular...