Numerical solution of the nonlinear Klein–Gordon equation using radial basis functions
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摘要
The nonlinear Klein–Gordon equation is used to model many nonlinear phenomena. In this paper, 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 (TPS) radial basis functions (RBF). 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.
论文关键词:Nonlinear Klein–Gordon equation,Collocation,Radial basis functions (RBF),Thin plate splines (TPS)
论文评审过程:Received 15 April 2007, Revised 10 December 2008, Available online 30 December 2008.
论文官网地址:https://doi.org/10.1016/j.cam.2008.12.011