A numerical method for solution of the two-dimensional sine-Gordon equation using the radial basis functions |
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| Authors: | Mehdi Dehghan Ali Shokri |
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| Affiliation: | Department of Applied Mathematics, Faculty of Mathematics and Computer Science, Amirkabir University of Technology, No. 424, Hafez Avenue, Tehran, Iran |
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| 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. |
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| Keywords: | Two-dimensional damped/undamped sine-Gordon equation Soliton Collocation Radial basis function (RBF) Thin plate splines (TPS) |
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