THE METHOD OF APPROXIMATE PARTICULAR SOLUTIONS FOR SOLVING ELLIPTIC PROBLEMS WITH VARIABLE COEFFICIENTS-Reference-Cited by-同舟云学术

THE METHOD OF APPROXIMATE PARTICULAR SOLUTIONS FOR SOLVING ELLIPTIC PROBLEMS WITH VARIABLE COEFFICIENTS

Published:2011-09 Issue:03 Volume:08 Page:545-559
ISSN:0219-8762
Container-title:International Journal of Computational Methods
language:en
Short-container-title:Int. J. Comput. Methods

Author:

CHEN C. S.¹,FAN C. M.²,WEN P. H.³

Affiliation:

1. Department of Mathematics, University of Southern Mississippi, Hattiesburg, MS 39406, USA

2. Department of Harbor and River Engineering, National Taiwan Ocean University, Keelung 20224, Taiwan

3. Department of Engineering, Queen Mary, University of London, London E1 4NS, UK

Abstract

A new version of the method of approximate particular solutions (MAPSs) using radial basis functions (RBFs) has been proposed for solving a general class of elliptic partial differential equations. In the solution process, the Laplacian is kept on the left-hand side as a main differential operator. The other terms are moved to the right-hand side and treated as part of the forcing term. In this way, the close-form particular solution is easy to obtain using various RBFs. The numerical scheme of the new MAPSs is simple to implement and yet very accurate. Three numerical examples are given and the results are compared to Kansa's method and the method of fundamental solutions.

Publisher

World Scientific Pub Co Pte Lt

Subject

Computational Mathematics,Computer Science (miscellaneous)

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0219876211002484

Reference12 articles.

1. The Numerical Evaluation of Particular Solutions for Poisson's Equation

2. C. S. Chen, C. M. Fan and J. Monroe, The Method of Fundamental Solutions — A Meshless Method, eds. Y. S. Smyrlis, C. S. Chen and A. Karageorghis (Dynamics Publisher, 2008) pp. 75–105.

3. Particular solutions of Laplacian, Helmholtz-type, and polyharmonic operators involving higher order radial basis functions

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