The Boundary Integral Equation Approach for Numerical Solution of the One-Dimensional Sine-Gordon Equation

被引：47

作者：

Dehghan, Mehdi ^{[1
]}

Mirzaei, Davoud ^{[1
]}

机构：

[1] Amirkabir Univ Technol, Dept Appl Math, Fac Math & Comp Sci, Tehran 15914, Iran

来源：

NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS | 2008年 / 24卷 / 06期

关键词：

boundary integral equation; dual reciprocity method; Sine-Gordon equation; conservation of energy;

D O I：

10.1002/num.20325

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This article describes a numerical method based on the boundary, integral equation and dual reciprocity method for solving the one-dimensional Sine-Gordon (SG) equation. The time derivative is approximated by the time-stepping method and a predictor-corrector scheme is employed to deal with the nonlinearity which appears in the problem. Numerical results are presented for some problems to demonstrate the usefulness and accuracy of this approach. In addition, the conservation of energy in SG equation is investigated. (C) 2008 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 24: 1405-1415, 2008

引用

页码：1405 / 1415

页数：11

共 38 条

[1] On the numerical solution of the sine-Gordon equation .1. Integrable discretizations and homoclinic manifolds [J].

Ablowitz, MJ ;

Herbst, BM ;

Schober, C .

JOURNAL OF COMPUTATIONAL PHYSICS, 1996, 126 (02) :299-314

[2] On the numerical solution of the sine-Gordon equation .2. Performance of numerical schemes [J].

Ablowitz, MJ ;

Herbst, BM ;

Schober, CM .

JOURNAL OF COMPUTATIONAL PHYSICS, 1997, 131 (02) :354-367

[3] A numerical method for the wave equation subject to a non-local conservation condition [J].

Ang, WT .

APPLIED NUMERICAL MATHEMATICS, 2006, 56 (08) :1054-1060

[4]

[Anonymous], INT J NONLINEAR SCI

[5]

[Anonymous], INT J SOIL DYN EARTH

[6]

[Anonymous], 2005, APPL NUMER ANAL COMP, DOI DOI 10.1002/ANAC.200410035

[7] FINITE-ELEMENT APPROXIMATION TO 2-DIMENSIONAL SINE-GORDON SOLITONS [J].

ARGYRIS, J ;

HAASE, M ;

HEINRICH, JC .

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 1991, 86 (01) :1-26

[8] Numerical solution of sine-Gordon equation by variational iteration method [J].

Batiha, B. ;

Noorani, M. S. M. ;

Hashim, I. .

PHYSICS LETTERS A, 2007, 370 (5-6) :437-440

[9] A third order numerical scheme for the two-dimensional sine-Gordon equation [J].

Bratsos, A. G. .

MATHEMATICS AND COMPUTERS IN SIMULATION, 2007, 76 (04) :271-282

[10] The solution of the two-dimensional sine-Gordon equation using the method of lines [J].

Bratsos, A. G. .

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2007, 206 (01) :251-277

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