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

Guang-Da Hu

Kybernetika (2018)

  • Volume: 54, Issue: 4, page 718-735
  • ISSN: 0023-5954

Abstract

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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 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.

How to cite

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Hu, Guang-Da. "Delay-dependent stability of Runge-Kutta methods for linear neutral systems with multiple delays." Kybernetika 54.4 (2018): 718-735. <http://eudml.org/doc/294173>.

@article{Hu2018,
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.},
author = {Hu, Guang-Da},
journal = {Kybernetika},
keywords = {neutral differential systems with multiple delays; delay-dependent stability; Runge–Kutta method; Lagrange interpolation; argument principle},
language = {eng},
number = {4},
pages = {718-735},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Delay-dependent stability of Runge-Kutta methods for linear neutral systems with multiple delays},
url = {http://eudml.org/doc/294173},
volume = {54},
year = {2018},
}

TY - JOUR
AU - Hu, Guang-Da
TI - Delay-dependent stability of Runge-Kutta methods for linear neutral systems with multiple delays
JO - Kybernetika
PY - 2018
PB - Institute of Information Theory and Automation AS CR
VL - 54
IS - 4
SP - 718
EP - 735
AB - 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.
LA - eng
KW - neutral differential systems with multiple delays; delay-dependent stability; Runge–Kutta method; Lagrange interpolation; argument principle
UR - http://eudml.org/doc/294173
ER -

References

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