In this paper, we design a domain decomposition algorithm for the two-dimensional parabolic equation with variable coefficient by using a larger spacing at interface points and the implicit scheme at the interior points, hence get an algorithm with the relaxed stability bounds. Then we prove the stability and analyze the accuracy of the algorithm by using the idea of maximum principle. Some results of numerical experiments are also provided.
"Domain decomposition algorithm for the parabolic equation with variable coefficient." Commun. Math. Sci. 2 (3) 391 - 402, September 2004.