Application of the dual reciprocity boundary integral equation technique to solve the nonlinear Klein-Gordon equation

被引：75
作者：
Dehghan, Mehdi [1 ]
Ghesmati, Arezou [1 ]
机构：
[1] Amirkabir Univ Technol, Fac Math & Comp Sci, Dept Appl Math, Tehran 15914, Iran
来源：
COMPUTER PHYSICS COMMUNICATIONS | 2010年 / 181卷 / 08期
关键词：
Boundary Integral Equation (BIE) method; Dual Reciprocity Boundary Element Method (DRBEM); Nonlinear Klein-Gordon equation (NLKG); Conservation of energy and momentum; Soliton solutions; FINITE-DIFFERENCE APPROXIMATIONS; RADIAL BASIS FUNCTIONS; NUMERICAL-SOLUTION; DECOMPOSITION METHOD; UNBOUNDED DOMAIN; WAVE-EQUATION; DRBEM MODEL; SUBJECT; SPECIFICATIONS; COMPACTONS;
D O I：
10.1016/j.cpc.2010.04.008
中图分类号：
TP39 [计算机的应用];
学科分类号：
081203 ; 0835 ;
摘要：
This paper aims to obtain approximate solutions of the Nonlinear Klein-Gordon (NLKG) equation by employing the Boundary Integral Equation (BIE) method and the Dual Reciprocity Boundary Element Method (DRBEM). This method is improved by using a predictor-corrector scheme to the nonlinearity which appears in the problem. We employ the time stepping scheme to approximate the time derivative, and the Linear Radial Basis Functions (LRBFs), are used in the Dual Reciprocity (DR) technique. To confirm the accuracy of the new approach, the numerical results of a Double-Soliton and a problem with inhomogeneous terms are compared with analytical solutions and for the examples possessing single and periodic waves, two conserved quantities associated to the (NLKG) equation, the energy and the momentum are investigated. (C) 2010 Elsevier B.V. All rights reserved.
引用
收藏
页码：1410 / 1416
页数：7
相关论文
共 63 条
[1]  
Ablowitz M J., 1990, Solitons, Nonlinear Evolution Equations and Inverse Scattering Transform
[2]  
Aliabadi M.H., 1993, ADV FORMULATIONS BOU
[3]  
Ang W-T, 2007, A beginner's course in boundary element methods
[4]   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
[5]   A dual-reciprocity boundary element solution of a generalized nonlinear Schrodinger equation [J].
Ang, WT ;
Ang, KC .
NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, 2004, 20 (06) :843-854
[6]  
[Anonymous], INT J NONLINEAR SCI
[7]  
[Anonymous], 1988, APPL MATH SCI
[8]   Solution of non-linear Klein-Gordon equation with a quadratic non-linear term by Adomian decomposition method [J].
Basak, Kartik Chandra ;
Ray, Pratap Chandra ;
Bera, Rasajit Kumar .
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, 2009, 14 (03) :718-723
[9]   A numerical method for the one-dimensional sine-Gordon equation [J].
Bratsos, A. G. .
NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, 2008, 24 (03) :833-844
[10]   On the Numerical Solution of the Klein-Gordon Equation [J].
Bratsos, A. G. .
NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, 2009, 25 (04) :939-951
1234567