Some Stability and Convergence of Additive Runge-Kutta Methods for Delay Differential Equations with Many Delays

Haiyan Yuan, Jingjun Zhao and Yang Xu

Journal of Applied Mathematics, 2012, vol. 2012, 1-18

Abstract:

This paper is devoted to the stability and convergence analysis of the additive Runge-Kutta methods with the Lagrangian interpolation (ARKLMs) for the numerical solution of a delay differential equation with many delays. GDN stability and D-Convergence are introduced and proved. It is shown that strongly algebraically stability gives D-Convergence DA, DAS, and ASI stability give GDN stability. Some examples are given in the end of this paper which confirms our results.

Date: 2012
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnljam:456814

DOI: 10.1155/2012/456814

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