多比例延迟微分方程Rosenbrock方法的渐近稳定性

Asymptotic Stability of Rosenbrock Methods for the Multi-pantograph Equation

主要讨论了用一类变步长Rosenbrock方法求解多比例延迟微分方程y′(t)=λy(t)+∑lk=1μky(qkt),λ,μk∈C,0<ql<…<q2<q1<1的数值稳定性,获得了Rosenbrock方法渐近稳定的充分条件。

This paper is concerned with the stability of Rosenbrock methods with variable stepsize applied tomulti-pamograph equationy＇（t）=λy（t）＋∑k=1^lμky（qkt）,λ,μk∈C,0〈q1〈…〈q2〈q1〈1. Weobtained the sufficient condtions of asymptotic stability of Rosenbrock methods.