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

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.