Truncation Error and Oscillation Property of
the Combined Compact Difference Scheme

Jun Zhang
Department of Computer Science
University of Kentucky
773 Anderson Hall
Lexington, KY 40506-0046, USA

Jennifer J. Zhao
Department of Mathematics and Statistics
University of Michigan at Dearborn
Dearborn, MI 48128-1491, USA

Abstract

We derive truncation error representation for the sixth order combined compact difference (CCD) scheme for discretizing a one dimensional partial differential equation. We also show that, for a model one dimensional convection diffusion equation, the CCD scheme produces numerical oscillatory solution, when the cell Reynolds number condition is violated. Numerical experiments are used to demonstrate and support our analysis.

Key words: combined compact difference scheme, numerical oscillation, convection diffusion equation.

Mathematics Subject Classification: 65N06, 65N12.

Download the compressed postscript file ccd.ps.gz, or the PDF file ccd.pdf.gz.
This paper has been published in Applied Mathematics and Computation Vol. 161, No. 1 pp. 241-251 (2005).

Technical Report 329-01, Department of Computer Science, University of Kentucky, Lexington, KY, 2001. This research was supported in part by the U.S. National Science Foundation under the grant CCR-9902022, CCR-9988165, CCR-0092532, and CCR-0117602.