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A numerical method for KdV equation using collocation and radial basis functions. (English) Zbl 1185.76832
Summary: Recently, there has been an increasing interest in the study of initial boundary value problems for Korteweg-de Vries (KdV) equations. In this paper, we propose a numerical scheme to solve the third-order nonlinear KdV equation using collocation points and approximating the solution using multiquadric (MQ) radial basis function (RBF). The scheme works in a similar fashion as finite-difference methods. Numerical examples are given to confirm the good accuracy of the presented scheme.

MSC:
76M25 Other numerical methods (fluid mechanics) (MSC2010)
76B25 Solitary waves for incompressible inviscid fluids
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