Zhilin Li & Yun-Qiu Shen
In 1993, Li and Mayo  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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Department of Mathematics, Western Washington University
Bellingham, WA 98225-9063, USA