A meshfree method for numerical solution of KdV equation

This paper formulates a meshfree radial basis functions (RBFs) collocation (Kansa) method for the numerical solution of the Korteweg-de Vries (KdV) equation. The accuracy of the method is assessed in terms of the errors in L∞, L2 and root mean square (RMS), number of nodes in the domain of influence, parameter-dependent RBFs time and spatial steps length. This approach has an edge over the traditional methods such as finite-difference and finite-element methods because it does not require a mesh to discretize the problem domain, and a set of scattered nodes in the domain of influence provided by initial data is required for the realization of the method. Numerical experiments demonstrate the accuracy and robustness of the method when applied to complicated nonlinear partial differential equations. In this work, three test problems are studied.