Stability of implicit one-block methods for delay differential equations

Abstract

This paper deals with the stability analysis of implicit one-block methods for the numerical solutions of the systems of delay differential equations (DDEs). We focus on the behavior of such methods when they are applied to the linear test problem y ′ (t)=Ly(t)+My(t−τ), t⩾0, y(t)=g(t), −τ⩽t⩽0 with τ>0 and L, M constant complex-value matrices. We show that an A-stable implicit one-block method preserves the asymptotic stability property of the analytical solutions of the system (0.1).