Generalized Rational Multi-step Method for Delay Differential Equations

This paper presents the generalized rational multi-step method for solving delay differential equations (DDEs). Here, we develop the r-step p-th order generalized multi-step method which is based on rational function approximation technique. The local truncation error and stability analysis are given. The delay argument is approximated using Lagrange interpolation. The applicability of this method has been demonstrated by numerical examples of DDEs with constant delay (HIV-1 infection model), time dependent delay and state dependent delays.