Kybernetika 54 no. 4, 718-735, 2018

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

Guang-Da HuDOI: 10.14736/kyb-2018-4-0718

Abstract:

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 differential systems with multiple delays. Based on the argument principle, sufficient conditions for delay-dependent stability of Runge-Kutta methods combined with Lagrange interpolation are presented. Numerical examples are given to illustrate the main results.

Keywords:

Runge-Kutta method, neutral differential systems with multiple delays, delay-dependent stability, Lagrange interpolation, argument principle

Classification:

65L05, 65L07, 65L20

paper.pdf

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