Fourth Mississippi State Conference on Differential Equations and Computational Simulations,
Electron. J. Diff. Eqns., Conf. 03, 1999, pp. 100-108.

A numerical method for solving heat equations involving interfaces

Zhilin Li & Yun-Qiu Shen

Abstract:
In 1993, Li and Mayo [3] gave a finite-difference method with second order accuracy for solving the heat equations involving interfaces with constant coefficients and discontinuous sources. In this paper, we expand their result by presenting a finite-difference method which allows each coefficient to take different values in different sub-regions of the interface. Our method is useful in physical applications, and has also second order accuracy.

Published July 10, 2000.
Math Subject Classifications: 65M06, 65M12, 65M15.
Key Words: Finite difference, Second order accuracy, Interface, Local coordinates.

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Zhilin Li
Center for Research in Scientific Computation
and Department of Mathematics, North Carolina State University
Raleigh, NC 27695-8205, USA

Yun-Qiu Shen
Department of Mathematics, Western Washington University
Bellingham, WA 98225-9063, USA
e-mail: yqshen@cc.wwu.edu

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