full
search.png

Search

close.png

Cancel

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

A. Karageorghis & I. Kyza

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

Published online: 2007-02

Preview Full PDF 3267 28686

Cited by

google scholar semantic scholar
Export citation
  • 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

  • Email address
  • BibTex
  • RIS
  • TXT
@Article{CiCP-2-501, author = {A. Karageorghis and I. Kyza}, 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 AU - A. Karageorghis & I. Kyza 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 and I. Kyza. (2007). Efficient Algorithms for Approximating Particular Solutions of Elliptic Equations Using Chebyshev Polynomials. Communications in Computational Physics. 2 (3). 501-521. doi:
Copy to clipboard
BibteX RIS TXT
The citation has been copied to your clipboard