Keywords : GP-Stability

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

Abbas Y. Al-Bayati; Ann J. Al-Sawoor; Reyadh S. Naoum

AL-Rafidain Journal of Computer Sciences and Mathematics, 2011, Volume 8, Issue 2, Pages 21-33
DOI: 10.33899/csmj.2011.163638

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).