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.

Download the compressed postscript file pennes1d.ps.gz, or the PDF file pennes1d.pdf.
This paper has been accepted for publication in Applied Mathematics and Computation

Technical Report 354-02, Department of Computer Science, University of Kentucky, Lexington, KY, 2002.

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.