Efficient Algorithms for Approximating Particular Solutions of Elliptic Equations Using Chebyshev Polynomials
Year: 2007
Communications in Computational Physics, Vol. 2 (2007), Iss. 3 : pp. 501–521
Abstract
In this paper, we propose efficient algorithms for approximating particular solutions of second and fourth order elliptic equations. The approximation of the particular solution by a truncated series of Chebyshev polynomials and the satisfaction of the differential equation lead to upper triangular block systems, each block being an upper triangular system. These systems can be solved efficiently by standard techniques. Several numerical examples are presented for each case.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2007-CiCP-7915
Communications in Computational Physics, Vol. 2 (2007), Iss. 3 : pp. 501–521
Published online: 2007-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 21
Keywords: Chebyshev polynomials Poisson equation biharmonic equation method of particular solutions.