A mesh free method using hyperinterpolation and fast Fourier transform for solving differential equations

Abstract

In this paper we propose a new method of deriving the particular solutions of differential equations by using the Sloan hyperinterpolation and fast Fourier transform. The special features of our approach are that a close form of particular solutions can be easily obtained and the matrix formulation for evaluating particular solution is not required. The method of fundamental solutions is used to solve the boundary value problems. The computational efficiency of the method is demonstrated by several numerical examples of Poisson's, modified Helmholtz, and diffusion equations.