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

Abstract EN

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.