Numerical Solution of Delay Differential Equations by Uniform Corrections to an Implicit Runge-Kutta Method.

Marino Zennaro; Alfredo Bellen

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Delay-dependent stability of Runge-Kutta methods for linear neutral systems with multiple delays

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In this paper, we are concerned with stability of numerical methods for linear neutral systems with multiple delays. Delay-dependent stability of Runge-Kutta methods is investigated, i. e., for delay-dependently stable systems, we ask what conditions must be imposed on the Runge-Kutta methods in order that the numerical solutions display stability property analogous to that displayed by the exact solutions. By means of Lagrange interpolation, Runge-Kutta methods can be applied to neutral...