A High Order Compact Boundary Value Method for
Solving One Dimensional Heat Equations

Haiwei Sun and Jun Zhang
Laboratory for High Performance Scientific Computing and Computer Simulation
Department of Computer Science
University of Kentucky
773 Anderson Hall
Lexington, KY 40506-0046, USA

Abstract

We combine fourth order boundary value methods (BVMs) for discretizing the temporal variable with fourth order compact difference scheme for discretizing the spatial variable to solve one dimensional heat equations. The resulting compact difference scheme achieves fourth order accuracy in both temporal and spatial variables, and is unconditionally stable due to the favorable stability property of BVMs. Numerical results are presented to demonstrate the accuracy and efficiency of the new compact difference scheme, compared to the standard second order Crank-Nicolson scheme.

Key words: Heat equation, compact difference scheme, BVMs, Crank-Nicolson scheme, unconditional stability.

Mathematics Subject Classification: 65N06, 65N55, 65F10.

Download the compressed postscript file cbvm1d.ps.gz, or the PDF file cbvm1d.pdf.gz.
This paper has been published in Numerical Methods for Partial Differential Equations, Vol. 19, No. 9, pp. 846--857, (2003).

Technical Report 333-02, Department of Computer Science, University of Kentucky, Lexington, KY, 2002.

This research was supported in part by the U.S. National Science Foundation under the grant CCR-9902022, CCR-9988165, and CCR-0092532, in part by the U.S. Department of Energy under grant DE-FG02-02ER45961, in part by the Japanese Research Organization for Information Science & Technology, and in part by the University of Kentucky Research Committee.