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

Authors:
Lixin Ge;Jun Zhang
Affiliations:
Department of Computer Science, University of Kentucky, 773 Anderson Hall, Lexington, KY;Department of Computer Science, University of Kentucky, 773 Anderson Hall, Lexington, KY
Venue:
Journal of Computational and Applied Mathematics
Year:
2002

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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.