A novel RBF collocation method using fictitious centres

Abstract

We propose a simple approach which considerably improves the performance of the well-known Kansa method for the solution of boundary value problems (BVPs). In the proposed approach, in contrast to the traditional Kansa method where the centres are placed in the closure of the domain of the BVP in question, the centres can be located outside it. We also employ a novel hybrid technique for the determination of the shape parameter in the radial basis functions used. Numerical examples in 2D and 3D are presented to demonstrate the effectiveness of the proposed method.