Journal of Applied Mathematics

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

Haiyan Yuan, Jingjun Zhao, and Yang Xu

Full-text: Open access

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.

Article information

Source
J. Appl. Math., Volume 2012 (2012), Article ID 456814, 18 pages.

Dates
First available in Project Euclid: 17 October 2012

Permanent link to this document
https://projecteuclid.org/euclid.jam/1350479348

Digital Object Identifier
doi:10.1155/2012/456814

Mathematical Reviews number (MathSciNet)
MR2910924

Zentralblatt MATH identifier
1244.65106

Citation

Yuan, Haiyan; Zhao, Jingjun; Xu, Yang. Some Stability and Convergence of Additive Runge-Kutta Methods for Delay Differential Equations with Many Delays. J. Appl. Math. 2012 (2012), Article ID 456814, 18 pages. doi:10.1155/2012/456814. https://projecteuclid.org/euclid.jam/1350479348


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