Center for Computational Sciences
University of Kentucky
Lexington, KY 40506-0045, USA
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.
Mathematics Subject Classification: 65M06, 65N12.
Technical Report 299-00, Department of Computer Science, University of Kentucky, Lexington, KY, 2000. This research was supported in part by the U.S. National Science Foundation under the grant CCR-9902022, and in part by the University of Kentucky Center for Computational Sciences.