两类隐式单块混合法

Two Classes of Implicit One-block Hybrid Methods

对解m维Stiff常徽分方程初值问题提出了可高度并行计算的r-点r+3阶A-稳定和r-点r+2阶L-稳定的两类隐式单块混合法，由此两类方法所导出的方程组可用“完全平方”迭代法解之，如使用r个处理机并行计算，则每个处理机上的LU－分解运算量为m3/3+O(m2)，文未给出了算例。

For the initial value problems of the stiff systems of m-dimensional ordinary differential equations, this paper presents two classes of implicit one-block hybrid methods with highly parallelism, in which,one class is r-point (r+3)-order A-stable methods, the other class is r-point (r+2)-order L-stable methods. For the equation systems produced by the two classes of methods, we use complete square iterative method to solve them. If parallel computer systems with r processors are used, then LU-decomposition operation amount is m3/3+O(m2) on each processor.The end in the paper gives numerical examples.