The Recursive Formulation of Particular Solutions for Some Elliptic PDEs with Polynomial Source Functions (Communications in Computational Physics, 2009)
In this paper we develop an efficient meshless method for solving inhomogeneous elliptic partial differential equations. We first approximate the source functionby Chebyshev polynomials. We then focus on how to find a polynomial particular solution when the source function is a polynomial. Through the principle of the methodof undetermined coefficients and a proper arrangement of the terms for the polynomial particular solution to be determined, the coefficients of the particular solutionsatisfy a triangular system of linear algebraic equations. Explicit recursive formulasfor the coefficients of the particular solutions are derived for different types of ellipticPDEs. The method is further incorporated into the method of fundamental solutionsfor solving inhomogeneous elliptic PDEs. Numerical results show that our approachis efficient and accurate.