Derivation of particular solutions using chebyshev polynomial based functions

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International Journal of Computational Methods, ISSN: 0219-8762, Vol: 4, Issue: 1, Page: 15-32

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Chen, C.S.; Lee, Sungwook; Huang, C.-S.
World Scientific Pub Co Pte Lt
Computer Science; Mathematics; particular solutions; method of fundamental solutions; radial basis functions; Chebyshev polynomial; meshless methods; multidimensional interpolation; Physical Sciences and Mathematics
article description
In this paper, we propose a simple and direct numerical procedure to obtain particular solutions for various types of differential equations. This procedure employs the power series expansion of a differential operator. Chebyshev polynomials are selected as basis functions for the approximation of the inhomogeneous terms of the given partial differential equation. This numerical scheme provides a highly efficient and accurate approximation for the evaluation of a particular solution for a variety of classes of partial differential equations. To demonstrate the effectiveness of the proposed scheme, we couple the method of fundamental solutions to solve a modified Helmholtz equation with irregular boundary configuration. The solutions were observed to have high accuracy. © 2007 World Scientific Publishing Company.