Radau IIA方法对比例延迟微分方程的渐近稳定性

研究Raudau IIA 方法用于求解比例延迟微分方程时的渐近稳定性。近年来比例延迟微分方程数值解的性质已被数位数学家所研究,他们使用的步长都是定步长,一般情况下将推导出较难分析的递推关系,在本文中出于理论和计算两方面的原因,我们研究强制变步长计算方案,这种解法得到不变阶差分方程。我们证明了Raudau IIA 方法是渐近稳定的。

Asymptotic Stability Properties of Radau IIA Methods for the Pantograph Delay Equation

This paper deals with the asymptotic stability analysis of Radau IIA methods for the pantograph delay equation. In recent years stability properties of numerical methods for this kind of equation have been studied by numerous authors who have considered meshes with fixed mesh. In general the developed techniques give rise to a non-ordinary recurrence relation. In this paper we study constrained variable stepsize schemes, suggested by theoretical and computational reasons, which lead to a non- stationary difference equation. We prove that Radau IIA methods are H-stable.