Stability criteria for exact and discrete solutions of neutral multidelay-integro-differential equations

This paper deals with the asymptotic stability of exact and discrete solutions of neutral multidelay-integro-differential equations. First, sufficient conditions are derived that guarantee the asymptotic stability of the continuous solutions. Then, adaptations of classical Runge-Kutta and linear multistep methods are suggested for solving these systems. Stability criteria are constructed for the asymptotic stability of these numerical methods and compared to the stability criteria derived for the continuous problem. We find that, under suitable conditions, these two classes of numerical methods retain the stability of the continuous systems, at least, for problems with commensurate delays. Finally, some numerical examples are given that illustrate the theoretical results.