Numerical solution of the nonlinear Klein-Gordon equation
نویسندگان
چکیده
This paper’s purpose is to provide a numerical scheme to approximate solutions of the nonlinear Klein-Gordon equation by applying the multiquadric quasi-interpolation scheme and the integrated radial basis function network scheme. Our scheme uses θ-weighted scheme for discretization of the temporal derivative and the integrated form of the multiquadric quasi-interpolation scheme for approximation of the unknown function and its spatial derivative. To confirm the accuracy and ability of the presented scheme, this scheme is applied on some test experiments and the numerical results have been compared with the exact solutions. Furthermore, it should be emphasized that with the presently available computing power, it has become possible to develop realistic mathematical models for the complicated problems in science and engineering. The mathematical description of various processes such as the nonlinear Klein-Gordon equation occurring in mathematical physics leads to a nonlinear partial differential equation. However, the mathematical model is only the first step towards the solution of the problem under consideration. The development of the well-documented, robust and reliable numerical technique for handing the mathematical model under consideration is the next step in the solution of the problem. This second step is at least as important as the first one. Therefore, the robustness, the efficiency and the reliability of the numerical technique have to be checked carefully.
منابع مشابه
Numerical solution of Klein-Gordon equation by using the Adomian's decomposition and variational iterative methods
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عنوان ژورنال:
- J. Computational Applied Mathematics
دوره 233 شماره
صفحات -
تاریخ انتشار 2010