常微分方程组初值问题的离散多分裂AOR波形松弛算法及其收敛性分析

Discrete Multisplitting AOR Waveform Relaxation Algorithm and Its Convergent Analysis for Initial Value Problem of Ordinary Differential Equations

本文首先基于交叉块分解的多分裂ＡＯＲ方法给出了波形松弛算法的一个推广，其次对等距时间结点，用隐式Ｅｕｌｅｒ方法并行数值求解各子方程组，最后，证明了多分裂ＡＯＲ波形松弛算法在一个固定的包含有限个时间点的区间上有收敛性。

This paper firstly gives an extended waveform relaxation algorithm by using multisplitting AOR method based on cross block decomposition of them,solves the subequations using implicit Euler method by parallel technique for equal time nodes,and ,lastly,proves the convergence of the method in a defined intemal which includesg finite time points.