Stability analysis of linear multistep methods for delay differential equations

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