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International Journal of Mathematics and Mathematical Sciences
Volume 9, Issue 3, Pages 447-458
http://dx.doi.org/10.1155/S0161171286000583

Stability analysis of linear multistep methods for delay differential equations

Department of Mathematical Sciences, University of Arkansas, Fayetteville, AR 72701, USA

Received 26 August 1985; Revised 28 January 1986

Copyright © 1986 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Stability properties of linear multistep methods for delay differential equations with respect to the test equation y(t)=ay(λt)+by(t),t0,0<λ<1, are investigated. It is known that the solution of this equation is bounded if and only if |a|<b and we examine whether this property is inherited by multistep methods with Lagrange interpolation and by parametrized Adams methods.