Journal of Applied Mathematics
- J. Appl. Math.
- Volume 2012 (2012), Article ID 456814, 18 pages.
Some Stability and Convergence of Additive Runge-Kutta Methods for Delay Differential Equations with Many Delays
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.
J. Appl. Math., Volume 2012 (2012), Article ID 456814, 18 pages.
First available in Project Euclid: 17 October 2012
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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