一类非线性微分方程单支θ-方法的稳定性

Stability of One-Leg-Methods for a class of nonlinear differential equations

首先在一般的H ilbert空间中研究了非线性微分方程单支θ-方法的数值稳定性,得到了该问题数值稳定性的一个充分条件.然后研究了单支θ-方法的代数稳定性,针对各种不同的情形,得到了该问题代数稳定性的一些结论,这些结论是文献[5]中相应结论的本质改进.

The numerical stability of One - Leg - Methods for nonlinear differential equations in Hilbert space are studied in this paper firstly, we gained a sufficient condition for the numerical stability of these problems. And then the algebraic stability of One - Leg - Methods is studied, according to various conditions, we gained some conclusions for the algebraic stability of these problems, these conclusions are the essential improvement of those in document[5 ].