Document Type

Article

Publication Date

9-1-2011

Department

Mathematics

School

Mathematics and Natural Sciences

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.

Comments

This is the peer reviewed version of the following article: "The Method of Approximate Particular Solutions for Solving Elliptic Problems with Variable Coefficients," which has been published in final form at 10.1142/S0219876211002484.

Publication Title

International Journal of Computational Methods

Volume

8

Issue

3

First Page

545

Last Page

559

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