International Journal of Mathematics and Mathematical Sciences 
Volume 9 (1986), Issue 3, Pages 447-458
doi:10.1155/S0161171286000583

Stability analysis of linear multistep methods for delay differential equations

V. L. Bakke and Z. Jackiewicz

 Department of Mathematical Sciences, University of Arkansas, Fayetteville 72701, AR, USA
Received 26 August 1985; Revised 28 January 1986

Abstract

Stability properties of linear multistep methods for delay differential equations with respect to the test equation y′(t)=ay(λt)+by(t),   t≥0,0<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.