Morgan-voyce polynomial solutions of functional differential equations and their applications

This thesis consists of six chapters. In the first chapter, the numerical solution methods of differntial-difference and delay differential equations, which belong to a class of functional differential equations, are given and the problems to be solved in study are introduced. In the second chapter, the fundamental properties of Morgan-Voyce polynomials are explained. In the third chapter, to find the solutions of differential-difference and delay differential equations in terms of Morgan-Voyce polynomials, the " Morgan-Voyce Collocation Method" along with residual error analysis is presented. In the fourth, we apply our method to five examples along with residual error analysis. In the last section, we discuss the obtained results.