一类非线性时滞微分代数方程的稳定性新方法以及隐式欧拉方法

摘要

Solving nonlinear problems through linearization. Although the linearization process is local, under certain conditions, linearization within the local neighborhood of some solution may not affect the original equations. Based on this idea, we consider the stability and asymptotic stability of a class of nonlinear delay differential-algebraic equations and numerical methods of implicit Euler methods by means of linearization process. Sufficient conditions for stability and asymptotic stability are obtained.%主要用线性化的方法处理解决非线性问题.虽然线性化的过程是局部的, 但是在某些条件下, 在某些解的局部邻域内的线性化不影响原方程的性质.基于这种思想, 研究了一类非线性时滞微分代数方程解的稳定性和渐进稳定性, 并讨论了隐式欧拉方法数值解稳定性和渐进稳定性的充分条件.