@Article{CiCP-5-942,
author = {J. Ding, H. Y. Tian and C. S. Chen},
title = {The Recursive Formulation of Particular Solutions for Some Elliptic PDEs with Polynomial Source Functions},
journal = {Communications in Computational Physics},
year = {2009},
volume = {5},
number = {5},
pages = {942--958},
abstract = {<p style="text-align: justify;">In this paper we develop an efficient meshless method for solving inhomogeneous elliptic partial differential equations. We first approximate the source function
by 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 method
of undetermined coefficients and a proper arrangement of the terms for the polynomial particular solution to be determined, the coefficients of the particular solution
satisfy a triangular system of linear algebraic equations. Explicit recursive formulas
for the coefficients of the particular solutions are derived for different types of elliptic
PDEs. The method is further incorporated into the method of fundamental solutions
for solving inhomogeneous elliptic PDEs. Numerical results show that our approach
is efficient and accurate.</p>},
issn = {1991-7120},
doi = {https://doi.org/},
url = {http://global-sci.org/intro/article_detail/cicp/7772.html}
}