郭瑜超^*

（  兰州大学数学与统计学院；  ）

摘要： 本文主要研究了抛物方程的紧式差分方程的加速分段并行迭代法。证明了迭代的收敛性，推出了网格加密时迭代的收敛性质。理论分析表明该迭代方法有很好的精度，并且有很好的收敛速度和渐进收敛性质。数值试验证明了理论分析的正确性，表明了算法的可行性和有效性。
关键词： 紧差分方程；并行迭代；渐进收敛性质

Guo Yuchao^*

（  School of mathematics and statistics, Lanzhou university Lanzhou；  ）

Abstract： This paper mainly studies the parallel algorithm of accelerative iteration for solving compact difference scheme of Parabolic PDE. Proves the convergence of the iteration. and the properties of asymptotic convergence. The theoretical analyses shows that the algorithm has good precision.In addition, the good convergent rate and properties of asymptotic convergence are obtained. The numerical examples show that the analyses are correct, and the algorithm is feasible and efficient.

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