Symbolic computation of high order compact difference schemes for three dimensional linear elliptic partial differential equations with variable coefficients

Lixin Ge, Jun Zhang

Research output: Contribution to journalArticlepeer-review

36 Scopus citations

Abstract

We present a symbolic computation procedure for deriving various high order compact difference approximation schemes for certain three dimensional linear elliptic partial differential equations with variable coefficients. Based on the Maple software package, we approximate the leading terms in the truncation error of the Taylor series expansion of the governing equation and obtain a 19 point fourth order compact difference scheme for a general linear elliptic partial differential equation. A test problem is solved numerically to validate the derived fourth order compact difference scheme. This symbolic derivation method is simple and can be easily used to derive high order difference approximation schemes for other similar linear elliptic partial differential equations.

Original languageEnglish
Pages (from-to)9-27
Number of pages19
JournalJournal of Computational and Applied Mathematics
Volume143
Issue number1
DOIs
StatePublished - Jun 1 2002

Keywords

  • Elliptic partial differential equations
  • Fourth order compact difference scheme
  • Maple software package
  • Symbolic derivation method

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics

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