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Split Local Artificial Boundary Conditions for the Two-Dimensional Sine-Gordon Equation on R2

Published online by Cambridge University Press:  20 August 2015

Houde Han  and
Zhiwen Zhang
Houde Han*
Affiliation:
Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China
Zhiwen Zhang*
Affiliation:
Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China
*
Corresponding author.Email:hhan@math.tsinghua.edu.cn
Email:zhangzhiwen02@mails.tsinghua.edu.cn
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Abstract

In this paper the numerical solution of the two-dimensional sine-Gordon equation is studied. Split local artificial boundary conditions are obtained by the operator splitting method. Then the original problem is reduced to an initial boundary value problem on a bounded computational domain, which can be solved by the finite difference method. Several numerical examples are provided to demonstrate the effectiveness and accuracy of the proposed method, and some interesting propagation and collision behaviors of the solitary wave solutions are observed.

Keywords

52B1065D1868U0568U07Sine-Gordon equationoperator splitting methodartificial boundary conditionsoli-tonunbounded domain
Type
Research Article
Information
Communications in Computational Physics , Volume 10 , Issue 5 , November 2011 , pp. 1161 - 1183
Copyright
Copyright © Global Science Press Limited 2011

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