抛物方程的校正型有限差分区域分解算法

摘要

研究抛物方程的校正型有限差分区域分解算法.用大空间步长的显格式预估内边界的值,然后以内边界的预估值作为方程的边界条件,用隐格式在子区域上并行计算方程的数值解,最后再用隐格式校正内边界的值.利用离散的最大值原理给出了算法的误差估计.数值实验表明本文所构造的算法具有良好的稳定性.%In this paper we investigate the corrected finite difference domain decomposition algorithm for parabolic equation. Firstly, the interface predictors are obtained by large space steplength explicit scheme, then subregion problems are solved by implicit scheme provided interface predictors serve the interior boundary data , at last the interface solution is recomputed by implicit scheme. The error estimation is obtained by the discrete maximum principle. Some numerical experiments are presented to show the stability of the proposed algorithm.