P-Stability of Linear Multistep Methods for Delay Retarded Differential Equations with Several Delays

Abstract

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 where are positive constants, and 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).

Keywords

• gp-stability
• linear multistep methods
• delay retarded differential equations