一种内向量选取下求解常微分方程组初值问题二步混合方法的代数稳定性

同一混合方法，在内向量的不同选取下，定义了不同的一般线性方法，因而它的代数稳定性是与内向量选取有关的。本文在把外向量定义成与函数ｆ（ｙ）有关的向量情况下，讨论了二步混合方法的代数稳定性，证明了任一二步四阶零稳定混合方法都不是代数稳定的。最后，作为例子，讨论了一步方法中的几个特殊方法。

Algebraic Stability of Two-step Hybrid Methods for Solving the Initial Value Problems of Ordinary Differential Equations under a Choice of the Internal Vector

We can define the different general linear methods under the different choices of internal vector with the same hybrid method , thus , the algebraic stability of hybrid methods is dependent on the choice of internal vector. In this paper , we discuss the algebraic stability of two-step hybrid methods with the external vector defined as a vector which is dependent on function f(y) . Furthermore, we prove that any two-step four-order hybird method which is zero-stable is not algebraic stable under the same condition. Finally, we give some examples for one-step hybrid methods.