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In this paper, we design a domain decomposition algorithm for the two-dimensional parabolic equation with variable coe-cient 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. cal explicit scheme by m 2 times. (2) has developed some techniques for the linear parabolic equation by using smaller time step ¢t=¢t=m in Saul'yev schemes at the interface points. The algorithm designed with the technique can increase the sta- bility bound of the classical explicit scheme by 2m times. The algorithm in (3) can increase the stability bound of the classical explicit scheme by 2m 2 times for the lin- ear parabolic equation, using the larger spacing in the x-direction implicit scheme and the y-direction implicit scheme at the interface points. The parallel e-ciency is not very high, because the algorithm needs the global communication while solving the tridiagonal linear algebraic equations. (4) has proposed a parallel flnite difierence method for parabolic PDEs, using either a high-order explicit scheme or a multistep explicit scheme with an intermediate mesh size H lying inside (h;HD) at the interface points. There are some other algorithms, see (5,6,7,8,9) for related discussions. However, much of the work has been directed at the linear parabolic equation, and the proof technique is a constructive method, which is unflt for the parabolic equation with variable a coe-cient. In this paper, we design a domain decomposition algorithm which can increase the stability bound of the classical explicit scheme by 4m 2 times for the parabolic equation with a variable coe-cient, and prove the stability and analyze the accuracy of the algorithm by using the idea of maximum principle. The framework of the paper is as follows. In the next section, a domain decompo- sition algorithm for the parabolic equation with a variable coe-cient is constructed. We use a larger spacing at interface points and the implicit scheme at the interior

Domain decomposition algorithm for the parabolic equation with variable coefficient