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.
"Nonlinear Stability and D-Convergence of Additive Runge-Kutta Methods for Multidelay-Integro-Differential Equations." Abstr. Appl. Anal. 2012 (SI12) 1 - 22, 2012. https://doi.org/10.1155/2012/854517