Convergence estimate of the RBF-based meshless method for initial-boundary value problem of wave equations

Abstract

This paper gives an order of convergence in applying the radial basis functions (RBF) as a meshless method for the initial-boundary value problem of wave equations. The analysis for a model wave equation shows that the convergence order of the proposed method is at least the same as which in finite difference method (FDM). For illustration, two examples are given to verify the accuracy and efficiency of the numerical solution by means of RBF and FDM.