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Stability of linear multistep methods for delay integro-differential equations

机译:时滞积分微分方程的线性多步法的稳定性

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摘要

This paper is concerned with the numerical solution of delay integro-differential equations. The adaptation of linear multistep methods is considered. The emphasis is on the linear stability of numerical methods. It is shown that every A-stable, strongly 0-stable linear multistep method of Pouzet type can preserve the delay-independent stability of the underlying linear systems. In addition, some delay-dependent stability conditions for the stability of numerical methods are also given.
机译:本文关注的是延迟积分微分方程的数值解。考虑了线性多步法的适应性。重点是数值方法的线性稳定性。结果表明,Pouzet类型的每个A稳定,强0稳定的线性多步方法都可以保留底层线性系统的时滞无关稳定性。此外,还给出了一些依赖于时滞的稳定性条件,用于数值方法的稳定性。

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