Numerical solution of the nonlinear Klein-Gordon equation using radial basis functions. (English) Zbl 1168.65398

Dehghan, Mehdi; Shokri, Ali

J. Comput. Appl. Math. 230, No. 2, 400-410 (2009).

Summary: The nonlinear Klein-Gordon equation is used to model many nonlinear phenomena. We propose a numerical scheme to solve the one-dimensional nonlinear Klein-Gordon equation with quadratic and cubic nonlinearity. Our scheme uses the collocation points and approximates the solution using thin plate splines radial basis functions. The implementation of the method is simple 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)

Keywords:

nonlinear Klein-Gordon equation; collocation; radial basis functions; thin plate splines

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