A numerical method for solution of the two-dimensional sine-Gordon equation using the radial basis functions. (English) Zbl 1155.65379
Summary: 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.
MSC:
| 65M70 | Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs |
| 35Q51 | Soliton equations |
| 35Q53 | KdV equations (Korteweg-de Vries equations) |
Keywords:
two-dimensional damped/undamped sine-Gordon equation; soliton; collocation; radial basis function (RBF); thin plate splines (TPS)References:
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