Commun. Comput. Phys., 2 (2007), pp. 501-521.


Efficient Algorithms for Approximating Particular Solutions of Elliptic Equations Using Chebyshev Polynomials

Andreas Karageorghis 1*, Irene Kyza 2

1 Department of Mathematics and Statistics, University of Cyprus, P.O. Box 20537, 1678 Nicosia, Cyprus.
2 Department of Mathematics, University of Crete, P.O. Box 2208, GR-714 09 Heraklion, Greece.

Received 3 April 2006; Accepted (in revised version) 25 August 2006
Available online 4 December 2006

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.

AMS subject classifications: 33A65, 65N35, 65N22, 35J05

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Key words: Chebyshev polynomials, Poisson equation, biharmonic equation, method of particular solutions.

*Corresponding author.
Email: andreask@ucy.ac.cy (A. Karageorghis), kyza@math.uoc.gr (I. Kyza)
 

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