Abstract and Applied Analysis
Volume 2012 (2012), Article ID 854517, 22 pages
http://dx.doi.org/10.1155/2012/854517
Research Article

Nonlinear Stability and D-Convergence of Additive Runge-Kutta Methods for Multidelay-Integro-Differential Equations

Haiyan Yuan,1,2 Jingjun Zhao,1 and Yang Xu1

1Department of Mathematics, Harbin Institute of Technology, Harbin 150001, China
2Department of Mathematics, Heilongjiang Institute of Technology, Harbin 150050, China

Received 30 December 2011; Accepted 19 February 2012

Academic Editor: Muhammad Aslam Noor

Copyright © 2012 Haiyan Yuan et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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 multidelay-integro-differential equations (MDIDEs). 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. A numerical example is given to illustrate the theoretical results.