Journal
MATHEMATICS AND COMPUTERS IN SIMULATION
Volume 79, Issue 3, Pages 700-715Publisher
ELSEVIER
DOI: 10.1016/j.matcom.2008.04.018
Keywords
Two-dimensional damped/undamped sine-Gordon equation; Soliton; Collocation; Radial basis function (RBF); Thin plate splines (TPS)
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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.
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