Title

Adaptive Method of Particular Solution for Solving 3D Inhomogeneous Elliptic Equations

Document Type

Article

Publication Date

9-1-2010

Department

Mathematics

Abstract

Recently, particular solutions using radial basis functions have been used as a basis for solving inhomogeneous partial differential equations as a one-stage approach without the need of finding homogeneous solutions. In this paper, we adopt a newly developed adaptive greedy algorithm to enhance the performance of the one-stage method and alleviate the difficulty of ill-conditioning of the resultant matrix. To demonstrate the effectiveness of coupling these two methods, we give two 3D examples with excellent numerical results.

Publication Title

International Journal of Computational Methods

Volume

7

Issue

3

First Page

499

Last Page

511