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

Mehdi Dehghan and Ali Shokri

Mathematics and Computers in Simulation (MATCOM), 2008, vol. 79, issue 3, 700-715

Abstract: The 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.

Keywords: Two-dimensional damped/undamped sine-Gordon equation; Soliton; Collocation; Radial basis function (RBF); Thin plate splines (TPS) (search for similar items in EconPapers)
Date: 2008
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Citations: View citations in EconPapers (10)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:79:y:2008:i:3:p:700-715

DOI: 10.1016/j.matcom.2008.04.018

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