A numerical method for KdV equation using collocation and radial basis functions

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.