偏微分方程的交替分组显式迭代方法

The Alternating Group Explicit Iterative Method for the Partial Differential Equation

求解复杂的偏微分方程或方程组时,对方程构造的差分格式可分为显式和隐式两大类。显式格式虽适用于并行计算,但其稳定性条件有严格限制;隐式格式稳定性虽好,但不能直接用于并行计算。本文利用交替分组显式算法的思想来设计隐式差分方程组的迭代解法,得到交替分组显式迭代法(AGEI)。这种方法可用于主对角占优的一般三对角方程组的迭代求解,不仅格式容易实现而且可直接进行并行计算。

In the solution of the complex partial differential equation or equations, it can be divided into the explicit schemes and the implicit schemes. Although the explicit schemes are suitable for the parallel computation, its stability is not well. And the implicit schemes has good stability, but can not be directly used for the parallel computation. However, the idea of an alternating group explicit iterative method can be used to design the implicit schemes. This method is suit to solve the tri - diagonal matrix.