Volume 2, Issue 3
Efficient Algorithms for Approximating Particular Solutions of Elliptic Equations Using Chebyshev Polynomials

A. Karageorghis & I. Kyza

DOI:

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

Published online: 2007-02

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  • 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.

  • Keywords

Chebyshev polynomials, Poisson equation, biharmonic equation, method of particular solutions.

  • AMS Subject Headings

33A65, 65N35, 65N22, 35J05

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CiCP-2-501, author = {}, title = {Efficient Algorithms for Approximating Particular Solutions of Elliptic Equations Using Chebyshev Polynomials}, journal = {Communications in Computational Physics}, year = {2007}, volume = {2}, number = {3}, pages = {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.

}, issn = {1991-7120}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/cicp/7915.html} }
TY - JOUR T1 - Efficient Algorithms for Approximating Particular Solutions of Elliptic Equations Using Chebyshev Polynomials JO - Communications in Computational Physics VL - 3 SP - 501 EP - 521 PY - 2007 DA - 2007/02 SN - 2 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/cicp/7915.html KW - Chebyshev polynomials, Poisson equation, biharmonic equation, method of particular solutions. AB -

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.

A. Karageorghis & I. Kyza. (2020). Efficient Algorithms for Approximating Particular Solutions of Elliptic Equations Using Chebyshev Polynomials. Communications in Computational Physics. 2 (3). 501-521. doi:
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