Application of a Numerical Method Using Radial Basis Functions to Nonlinear Partial Differential Equations

In this paper, we propose a meshfree method for numerical solution of various classes of partial differential equations (PDEs), such as the Boussinesq system, Drinefel'd-Sokolov-Wilson equations, and Hirota-Satsuma coupled KdV system. The meshfree algorithm is based on scattered data interpolation along with approximating functions known as radial basis functions (RBFs). The meshfree technique does not require space discretization. A set of scattered nodes provided by initial data is used for solution of the problem. Accuracy of the method is estimated in terms of the error norms L , L_{∞}, number of nodes in the domain of influence, time step size, parameter dependent and parameter independent RBFs, the numerical validation for the above mentioned three types of PDEs is given to check performance of the new approach.