GP-stability of linear multistep methods for delay retarded differential equations with several delays

Abstract EN

This paper modifies the numerical solution of initial value problems of the Delay Differential Equations (DDEs) by making it deals with Retarded Differential Equations (RDEs) with several delays Y (t) = f (t, y (t), y (t - τ1) ( t- τ2),…,y (t- τu)), t>0 y (t)= ∅ (t), t<0 where τ1,τ2,…,τu are positive constants, ∅ and f denote given vector-valued functions.

The stability behaviors of linear multistep method for RDEs is studied and it is proved that the linear multistep method is GP-stable if it is A-stable for Ordinary Differential Equations (ODEs).