An analysis of the finite-difference method for one-dimensional Klein-Gordon equation on unbounded domain

被引：19

作者：

Han, Houde ^{[1
]}

Zhang, Zhiwen ^{[1
]}

机构：

[1] Tsinghua Univ, Dept Math Sci, Beijing 100084, Peoples R China

来源：

APPLIED NUMERICAL MATHEMATICS | 2009年 / 59卷 / 07期

关键词：

Artificial Boundary Condition (ABC); Unbounded domain; Energy method; Fast algorithm; Discrete Artificial Boundary Condition (DABC); ABSORBING BOUNDARY-CONDITIONS; SCHRODINGER-EQUATION; APPROXIMATIONS; SIMULATION; SCHEMES; SYSTEMS; WAVES;

D O I：

10.1016/j.apnum.2008.10.005

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The numerical solution of the one-dimensional Klein-Gordon equation on an unbounded domain is analyzed in this paper. Two artificial boundary conditions are obtained to reduce the original problem to an initial boundary value problem on a bounded computational domain, which is discretized by an explicit difference scheme. The stability and convergence of the scheme are analyzed by the energy method. A fast algorithm is obtained to reduce the Computational cost and a discrete artificial boundary condition (DABC) is derived by the Z-transform approach. Finally, we illustrate the efficiency of the proposed method by several numerical examples. (C) 2008 IMACS. Published by Elsevier B.V. All rights reserved.

引用

页码：1568 / 1583

页数：16

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