A numerical method for solution of the two-dimensional sine-Gordon equation using the radial basis functions

被引：352

作者：

Dehghan, Mehdi ^{[1
]}

Shokri, Ali ^{[1
]}

机构：

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

来源：

MATHEMATICS AND COMPUTERS IN SIMULATION | 2008年 / 79卷 / 03期

关键词：

Two-dimensional damped/undamped sine-Gordon equation; Soliton; Collocation; Radial basis function (RBF); Thin plate splines (TPS);

D O I：

10.1016/j.matcom.2008.04.018

中图分类号：

TP39 [计算机的应用];

学科分类号：

081203 ; 0835 ;

摘要：

ne nonlinear sine-Gordon equation arises in various problems in science and engineering. In this paper, we propose a numerical scheme to solve the two-dimensional damped/undamped sine-Gordon equation. The proposed scheme is based on using collocation points and approximating the solution employing the thin plate splines (TPS) radial basis function (RBF). The new scheme works in a similar fashion as finite difference methods. Numerical results are obtained for various cases involving line and ring solitons. (C) 2008 IMACS. Published by Elsevier B.V. All tights reserved.

引用

页码：700 / 715

页数：16

共 46 条

[1] A collocation method using new combined radial basis functions of thin plate and multiquadraic types [J].

Ahmed, S. G. .

ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS, 2006, 30 (08) :697-701

[2]

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

[3] 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

[4] AN ENGINEERS GUIDE TO SOLITON PHENOMENA - APPLICATION OF THE FINITE-ELEMENT METHOD [J].

ARGYRIS, J ;

HAASE, M .

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 1987, 61 (01) :71-122

[5] 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

[6] 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

[7] A modified predictor-corrector scheme for the two-dimensional sine-Gordon equation [J].

Bratsos, A. G. .

NUMERICAL ALGORITHMS, 2006, 43 (04) :295-308

[8] A meshless method for free vibration analysis of circular and rectangular clamped plates using radial basis function [J].

Chen, JT ;

Chen, IL ;

Chen, KH ;

Lee, YT ;

Yeh, YT .

ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS, 2004, 28 (05) :535-545

[9]

CHRISTIANSEN PL, 1979, Z ANGEW MATH MECH, V59, pT30

[10] NUMERICAL STUDY OF 2+1 DIMENSIONAL SINE-GORDON SOLITONS [J].

CHRISTIANSEN, PL ;

LOMDAHL, PS .

PHYSICA D, 1981, 2 (03) :482-494

← 1 2 3 4 5 →