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Delay-dependent stability analysis of multistep methods for delay differential equations

Delay-dependent stability analysis of multistep methods for delay differential equations This paper deals with the delay-dependent stability of numerical methods for delay differential equations. First, a stability criterion of Runge-Kutta methods is extended to the case of general linear methods. Then, linear multistep methods are considered and a class of τ(0)-stable methods are found. Later, some examples of τ(0)-stable multistep multistage methods are given. Finally, numerical experiments are presented to confirm the theoretical results. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Mathematicae Applicatae Sinica Springer Journals

Delay-dependent stability analysis of multistep methods for delay differential equations

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Publisher
Springer Journals
Copyright
Copyright © 2009 by Institute of Applied Mathematics, Academy of Mathematics and System Sciences, Chinese Academy of Sciences and Springer Berlin Heidelberg
Subject
Mathematics; Theoretical, Mathematical and Computational Physics; Math Applications in Computer Science; Applications of Mathematics
ISSN
0168-9673
eISSN
1618-3932
DOI
10.1007/s10255-009-8816-8
Publisher site
See Article on Publisher Site

Abstract

This paper deals with the delay-dependent stability of numerical methods for delay differential equations. First, a stability criterion of Runge-Kutta methods is extended to the case of general linear methods. Then, linear multistep methods are considered and a class of τ(0)-stable methods are found. Later, some examples of τ(0)-stable multistep multistage methods are given. Finally, numerical experiments are presented to confirm the theoretical results.

Journal

Acta Mathematicae Applicatae SinicaSpringer Journals

Published: Sep 8, 2009

References