Efficient algorithms for approximating particular solutions of elliptic equations using Chebyshev polynomials

Andreas Karageorghis (Lead / Corresponding author), Irene Kyza

Research output: Contribution to journalArticlepeer-review

16 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)501-521
Number of pages21
JournalCommunications in Computational Physics
Volume2
Issue number3
Publication statusPublished - Jun 2007

Keywords

  • Biharmonic equation
  • Chebyshev polynomials
  • Method of particular solutions
  • Poisson equation

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