Legendre wavelet solutions of linear and nonlinear ordinary delay differential equations

This thesis presents the Legendre wavelet method to solve initial value problems involving linear and nonlinear ordinary delay differential equations. The differential equations together with the given initial conditions are transformed into a system of algebraic equations by using operational matrix of differentiation. Then the approximate solution is obtained from the function approximation with the coefficients obtained from this system of equations. This method is applied to several types of delay differential equations. The results are presented in terms of graphs. The solutions are compared with the analytical solution and numerical solutions in the literature when available. It is observed that the proposed method is a very effective and suitable approach in order to obtain either the exact or the approximate solutions to indicated types of differential equations. Keywords: Legendre Wavelets, Neutral Differential Equations, Nonlinear Ordinary Differential Equations, Variable Delay, Proportional Delay.