Instability of Runge-Kutta methods when applied to linear systems of delay differential equations

摘要

This paper investigates the stability of Runge-Kutta methods when they are applied to the complex linear system of delay differential equations $y^{prime }left( tright) =Lyleft( tright) +Myleft( t-1right) $ , where $L,Min mathbb{C}^{dtimes d}$ . We prove that no Runge-Kutta method preserves asymptotic stability.