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

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 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.