求解比例延迟微分方程的Rosenbrock方法的渐近稳定性(英文)

Asymptotic stability of Rosenbrock methods for pantograph equation

本文讨论了一类Rosenbrock方法求解比例延迟微分方程,y′(t)=λy(t)+μy(qt),λ,μ∈C,0<q<1的数值渐近稳定性。

This paper is concerned with the asymptotic stability of the Rosenbrock methods for the pantograph equation y′(t)=λy(t)+μy(qt),λ,μ∈C,0<q<1.It is shown that A-stable Rosenbrock method can inherit the asymptotic stability of underlying linear equation.