Abstract
This paper studies the asymptotic stability of the two-step Runge-Kutta methods for neutral delay integro differential-algebraic equations with many delays. It proves that A-stable two-step Runge-Kutta methods are asymptotically stable for neutral delay integro differential-algebraic equations with many delays.
Highlights
The stability of numerical methods for delay differential equations has been intensively studied in [1,2,3] for many years
This paper studies the asymptotic stability of the two-step Runge-Kutta methods for neutral delay integro differential-algebraic equations with many delays
Zhu and Petzold investigated the asymptotic stability of neutral delay differential equations with θ-methods, RungeKutta methods, BDF methods, and linear multistep methods [7]
Summary
The stability of numerical methods for delay differential equations has been intensively studied in [1,2,3] for many years. These equations appeared in a wide variety of scientific and engineering fields, such as circuit analysis, computeraided design power systems, and optimal control. Zhang and Vandewalle [14] gave the stability criteria for exact and discrete solution of neutral multidelay integro differential equations. We focus on the asymptotic stability of numerical methods for neutral delay integro differentialalgebraic equations with many delays.
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