Finite element methods for partial Volterra integro-differential equations on two-dimensional unbounded spatial domains

doi:10.1016/j.amc.2006.08.004

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	Finite element methods for partial Volterra integro-differential equations on two-dimensional unbounded spatial domains
	Ma, Jingtang
	2007-03-01
发表期刊	APPLIED MATHEMATICS AND COMPUTATION
ISSN	0096-3003
卷号	186 期号:1 页码:598-609
摘要	The precise and effective way for solving a partial Volterra integro-differential equation on unbounded spatial domain is to derive artificial boundary conditions for some feasible and prescribed computational domain. Thus the unsolvable problem on unbounded domain is converted to the computational problem on bounded domain, which is often called reduced problem. A feasible numerical method will then be applied to solve the reduced problem with the artificial boundary conditions which often exhibit "nonlocal" properties. In this paper, the finite element method for the spatial space and the recently developed discontinuous Galerkin time-stepping method for the temporal space are considered to solve the reduced problem. The convergence rate, explicitly with those interesting parameters: spatial grid-size h, temporal mesh-size k, the location of the artificial boundary d, and the truncation number M, is obtained. This paper is the first theoretical analysis of the numerical methods for Volterra integro-differential equations on unbounded spatial domains. (c) 2006 Elsevier Inc. All rights reserved.
关键词	partial Volterra integro-differential equations unbounded spatial domain artificial boundary conditions discontinuous Galerkin time-stepping methods finite element methods
DOI	10.1016/j.amc.2006.08.004
语种	英语
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000245999000063
出版者	ELSEVIER SCIENCE INC
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/4180
专题	中国科学院数学与系统科学研究院
通讯作者	Ma, Jingtang
作者单位	Chinese Acad Sci, Inst Computat Math, Acad Math & Syst Sci, Beijing 100080, Peoples R China
推荐引用方式 GB/T 7714	Ma, Jingtang. Finite element methods for partial Volterra integro-differential equations on two-dimensional unbounded spatial domains[J]. APPLIED MATHEMATICS AND COMPUTATION,2007,186(1):598-609.
APA	Ma, Jingtang.(2007).Finite element methods for partial Volterra integro-differential equations on two-dimensional unbounded spatial domains.APPLIED MATHEMATICS AND COMPUTATION,186(1),598-609.
MLA	Ma, Jingtang."Finite element methods for partial Volterra integro-differential equations on two-dimensional unbounded spatial domains".APPLIED MATHEMATICS AND COMPUTATION 186.1(2007):598-609.