A Two Level Finite Difference Scheme for
One Dimensional Pennes' Bioheat Equation

Jennifer J. Zhao
Department of Mathematics and Statistics
University of Michigan-Dearborn
Dearborn, MI 48374, USA
and
Jun Zhang and Ning Kang
Laboratory for High Performance Scientific Computing and Computer Simulation
Department of Computer Science
University of Kentucky
Lexington, KY 40506-0046, USA
and
Fuqian Yang
Department of Chemical and Materials Engineering
University of Kentucky
Lexington, KY 40506-0046, USA

Abstract

We develop a new two level finite difference scheme for the 1D Pennes' bioheat equation. We further prove that the scheme is stable and convergent unconditionally. Numerical experiments for a skin heating model are conducted.

Key words: bioheat transfer, Pennes' equation, finite difference.

Mathematics Subject Classification: 90C10, 80A20, 65M06.

This paper has been published in Applied Mathematics and Computation, Vol. 171, pp. 320-331 (2005). Download the published paper in a PDF file zhao-etal05a.pdf.

The paper was published as Technical Report 354-02, Department of Computer Science, University of Kentucky, Lexington, KY, 2002. Download the compressed postscript file pennes1d.ps.gz, or the PDF file pennes1d.pdf.

The research of Jennifer J. Zhao was supported in part by the U.S. National Science Foundation under grant CCR-0117602. The work of Jun Zhang and Ning Kang was supported in part by the U.S. National Science Foundation under the grant CCR-9902022, CCR-9988165, CCR-0092532, and ACI-0202934, in part by the U.S. Department of Energy Office of Sceince 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.