# American Institute of Mathematical Sciences

2007, 2007(Special): 956-964. doi: 10.3934/proc.2007.2007.956

## Numerical solutions for a coupled parabolic equations arising induction heating processes

 1 Department of Mathematics, Washington State University, P.O. Box 643113, Pullman, WA 99164-3113, United States 2 Department of Mathematics, Washington State University, Pullman, WA 99164, United States

Received  August 2006 Revised  July 2007 Published  September 2007

In this paper we study the numerical solution for a coupled parabolic equations. The system is derived from an induction heating process. An implicit finite-difference scheme for a coupled parabolic system is proposed and analyzed. Some numerical experiments are performed. We found that the numerical solutions do match the theoretical results obtained from the previous study. Moreover, some numerical results show new phenomenon which has not been proved up to now.
Citation: Dong Sun, V. S. Manoranjan, Hong-Ming Yin. Numerical solutions for a coupled parabolic equations arising induction heating processes. Conference Publications, 2007, 2007 (Special) : 956-964. doi: 10.3934/proc.2007.2007.956
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