Differential quadrature solution of nonlinear Klein-Gordon and sine-Gordon equations

Pekmen B., TEZER M.

COMPUTER PHYSICS COMMUNICATIONS, vol.183, no.8, pp.1702-1713, 2012 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 183 Issue: 8
  • Publication Date: 2012
  • Doi Number: 10.1016/j.cpc.2012.03.010
  • Journal Name: COMPUTER PHYSICS COMMUNICATIONS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.1702-1713
  • Keywords: Klein-Gordon equation, Sine-Gordon equation, Differential quadrature method, RADIAL BASIS FUNCTIONS, VARIATIONAL ITERATION METHOD, NUMERICAL-SOLUTION, SOLITONS, APPROXIMATION, COLLOCATION
  • Middle East Technical University Affiliated: Yes

Abstract

Differential quadrature method (DQM) is proposed to solve the one-dimensional quadratic and cubic Klein-Gordon equations, and two-dimensional sine-Gordon equation. We apply DQM in space direction and also blockwise in time direction. Initial and derivative boundary conditions are also approximated by DQM. DQM provides one to obtain numerical results with very good accuracy using considerably small number of grid points. Numerical solutions are obtained by using Gauss-Chebyshev-Lobatto (GCL) grid points in space intervals, and GCL grid points in each equally divided time blocks. (C) 2012 Elsevier B.V. All rights reserved.