A one-stage meshless method for nonhomogeneous Cauchy problems of elliptic partial differential equations with variable coefficients

Abstract

A one-stage meshless method is devised for solving Cauchy boundary value problems of elliptic partial differential equations (PDEs) with variable coefficients. The main idea is to approximate an unknown solution using a linear combination of fundamental solutions and radial basis functions. Compared with the two-stage method of particular solution, the proposed method can deal with more general elliptic PDEs with variable coefficients. Several numerical results in both two- and three-dimensional space show that our proposed method is accurate and effective.