Kansa RBF collocation method with auxiliary boundary centres for high order BVPs

Abstract

In this study we apply a Kansa-radial basis function (RBF) collocation method to 2D and 3D boundary value problems (BVPs) governed by high order partial differential equations (PDEs) of order 2N where N∈N,N≥3. As in such problems there are N boundary conditions (BCs), N distinct sets of boundary centres are needed. These could all be placed on the boundary with each set being different to the other or, alternatively, each set of boundary centres could be placed on a corresponding distinct curve surrounding the boundary of the problem. We apply these approaches to several 2D and 3D high order BVPs.