一阶常微分方程系统的并行算法及收敛性

Parallel Algorithms and Convergence for One Order Ordinary Differential Equations

构造了一类关于一阶微分方程系统初值问题的并行松弛迭代方法，对于系数矩阵A为M-矩阵时，证明了方法的收敛性．并通过实例计算和数值分析，发现迭代步骤并不随问题维数的增加而急剧增加，这说明方法是收敛的和稳定的．

A parallel iteration algorithm for initial value problems for an order ordinary differential equations is proposed. The convergence is proved when the factor matrax is M-matrix. Numerical experiments also show the convergence and stability of the algorithm.