Different types of delay different equations numerical solutions

This thesis forms threee parts which contains generally delay differential equation.In the First part, the fundamental definition of delay differential equation is presented and it is placed with modelling concerning about this differential equation and also using area related about it.In the Second part, some definiton and theorems are given in order to solve the system of delay differential equation and the solution of this system of the differential equation is tried to obtain using by the Lambert Function.In the Third part, the approximate solution of the delay differential equation is obtained by using of the Adomian and Differential Transform Method. Additionally the stability analysis of the delay differential equation is made by means of the Euler and Explicit Euler Methods