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A numerical method for solution of the two-dimensional sine-Gordon equation using the radial basis functions

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  • Dehghan, Mehdi
  • Shokri, Ali

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.

Suggested Citation

  • Dehghan, Mehdi & Shokri, Ali, 2008. "A numerical method for solution of the two-dimensional sine-Gordon equation using the radial basis functions," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(3), pages 700-715.
    • Handle: RePEc:eee:matcom:v:79:y:2008:i:3:p:700-715
    DOI: 10.1016/j.matcom.2008.04.018
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    References listed on IDEAS

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    1. Dehghan, Mehdi, 2006. "Finite difference procedures for solving a problem arising in modeling and design of certain optoelectronic devices," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 71(1), pages 16-30.
    2. Sheng, Q. & Khaliq, A.Q. M. & Voss, D.A., 2005. "Numerical simulation of two-dimensional sine-Gordon solitons via a split cosine scheme," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 68(4), pages 355-373.
    3. Bratsos, A.G., 2007. "A third order numerical scheme for the two-dimensional sine-Gordon equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 76(4), pages 271-282.
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    Cited by:

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