检索结果-南通市图书馆

HERMITE WENO SCHEMES WITH strong stability preserving MULTI-STEP TEMPORAL DISCRETIZATION METHODS FOR CONSERVATION LAWS

维普期刊数据库

同方期刊数据库评论

在线全文

学校读者我要写书评

暂无评论

Journal of Computational Mathematics 2017年第1期35卷 52-73页

作者： Xiaofeng Cai Jun Zhu Jianxian Qiu School of Mathematical Sciences Xiamen University Xiamen Fujian 361005 China College of Science Nanjing University of Aeronautics and Astronautics Nanjing Jiangsu 210016 China School of Mathematical Sciences and Fujian Provincial Key Laboratory of Mathematical Modeling and High-Performance Scientific Computation Xiamen University Xiamen Fujian 361005 China

Based on the work of Shu [SIAM J. Sci. Stat. Comput, 9 （1988）, pp.1073-1084], we construct a class of high order multi-step temporal discretization procedure for finite volume Hermite weighted essential non-oscillatory （HWENO） methods to solve hyperbolic conservation laws. The key feature of the multi-step temporal discretization procedure is to use variable time step with strong stability preserving （SSP）. The multi-step tem- poral discretization methods can make full use of computed information with HWENO spatial discretization by holding the former computational values. Extensive numerical experiments are presented to demonstrate that the finite volume HWENO schemes with multi-step diseretization can achieve high order accuracy and maintain non-oscillatory properties near discontinuous region of the solution.

关键词： Key words: Multi-step temporal discretization Hermite weighted essentially non-oscillatoryscheme Uniformly high order accuracy strong stability preserving Finite volume scheme.

ODE-Based Multistep Schemes for Backward Stochastic Differential Equations

在线全文

维普期刊数据库

学校读者我要写书评

暂无评论

Numerical Mathematics(Theory,Methods and Applications) 2023年第4期16卷 1053-1086页

作者： Shuixin Fang Weidong Zhao School of Mathematics&Institute of Finance Shandong UniversityJinanShandong 250100P.R.China

In this paper,we explore a new approach to design and analyze numerical schemes for backward stochastic differential equations(BSDEs).By the nonlinear Feynman-Kac formula,we reformulate the BSDE into a pair of reference ordinary differential equations(ODEs),which can be directly discretized by many standard ODE solvers,yielding the corresponding numerical schemes for *** particular,by applying strong stability preserving(SSP)time discretizations to the reference ODEs,we can propose new SSP multistep schemes for *** analyses are rigorously performed to prove the consistency,stability and convergency of the proposed SSP multistep *** experiments are further carried out to verify our theoretical results and the capacity of the proposed SSP multistep schemes for solving complex associated problems.

关键词： Backward stochastic differential equation parabolic partial differential equation strong stability preserving linear multistep scheme high order discretization

A Discontinuous Galerkin Method with Penalty for One-Dimensional Nonlocal Diffusion Problems

在线全文

维普期刊数据库

学校读者我要写书评

暂无评论

Communications on Applied Mathematics and Computation 2020年第1期2卷 31-55页

作者： Qiang Du Lili Ju Jianfang Lu Xiaochuan Tian Department of Applied Physics and Applied Mathematics Columbia UniversityNew YorkNY 10027USA Department of Mathematics University of South CarolinaColumbiaSC 29208USA South China Research Center for Applied Mathematics and Interdisciplinary Studies South China Normal UniversityGuangzhou 510631China Department of Mathematics University of Texas at AustinAustinTX 78712USA

There have been many theoretical studies and numerical investigations of nonlocal diffusion(ND)problems in recent *** this paper,we propose and analyze a new discontinuous Galerkin method for solving one-dimensional steady-state and time-dependent ND problems,based on a formulation that directly penalizes the jumps across the element interfaces in the nonlocal *** show that the proposed discontinuous Galerkin scheme is stable and ***,the local limit of such DG scheme recovers classical DG scheme for the corresponding local diff usion problem,which is a distinct feature of the new formulation and assures the asymptotic compatibility of the *** tests are also presented to demonstrate the eff ectiveness and the robustness of the proposed method.

关键词： Nonlocal diff usion Discontinuous Galerkin method Interior penalty Asymptotic compatibility strong stability preserving

High Order Semi-implicit Multistep Methods for Time-Dependent Partial Differential Equations

在线全文

维普期刊数据库

学校读者我要写书评

暂无评论

Communications on Applied Mathematics and Computation 2021年第4期3卷 701-718页

作者： Giacomo Albi Lorenzo Pareschi Computer Science Department University of VeronaVerona 37134Italy Mathematics and Computer Science Department University of FerraraFerrara 44121Italy

We consider the construction of semi-implicit linear multistep methods that can be applied to time-dependent PDEs where the separation of scales in additive form,typically used in implicit-explicit(IMEX)methods,is not *** shown in Boscarino et al.(***.68:975-1001,2016)for Runge-Kutta methods,these semi-implicit techniques give a great flexibility,and allow,in many cases,the construction of simple linearly implicit schemes with no need of iterative *** this work,we develop a general setting for the construction of high order semi-implicit linear multistep methods and analyze their stability properties for a prototype lineal'advection-diffusion equation and in the setting of strong stability preserving(SSP)*** findings are demonstrated on several examples,including nonlinear reaction-diffusion and convection-diffusion problems.

关键词： Semi-implicit methods Implicit-explicit methods Multistep methods strong stability preserving High order accuracy