Abstract
We consider a linear homogeneous system of neutral delay differential equations with a constant delay whose zero solution is asymptotically stable independent of the value of the delay, and discuss the stability of collocation-based Runge-Kutta methods for the system. We show that anA-stable method preserves the asymptotic stability of the analytical solutions of the system whenever a constant step-size of a special form is used.
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Koto, T. A stability property of A-stable collocation-based Runge-Kutta methods for neutral delay differential equations. Bit Numer Math 36, 855–859 (1996). https://doi.org/10.1007/BF01733796
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DOI: https://doi.org/10.1007/BF01733796