ABSTRACT
This chapter aims to show how transient probabilities for any model can be conveniently obtained numerically. The classical continuous Runge-Kutta methods are widely applied to compute the numerical solutions of delay differential equations without impulsive perturbations. The system multiplication method, Runge-Kutta, and Adams methods are compared, and the way of obtaining solutions of prescribed accuracy is outlined for the methods which numerically integrate the differential equation. The effectiveness of the Adams method technique is helping for the treatment of problems based on its attractive properties and an efficient technique. It deals with the algebraic nonlinear systems. The Adams method is a predictor-corrector and multi-step method. The principle behind using this method is the use of the past calculated values of probability to build a polynomial that approximates the derivative function and extrapolate this into the next interval.
