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A numerical method for one-dimensional nonlinear sine-Gordon equation using collocation and radial basis functions. (English) Zbl 1135.65380

Summary: 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 radial basis function. 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.

MSC:

65M70 Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs
35Q53 KdV equations (Korteweg-de Vries equations)
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