A numerical method for one-dimensional nonlinear Sine-Gordon equation using collocation and radial basis functions

In this article, we propose a numerical scheme to solve the one-dimensional undamped Sine-Gordon equation using collocation points and approximating the solution using Thin Plate Splines (TPS) radial basis function (RBF). The scheme works in a similar fashion as finite difference methods. The results of numerical experiments are presented and are compared with analytical solutions to confirm the good accuracy of the presented scheme. (c) 2007 Wiley Periodicals, Inc.