الفهرس 
Preface
Delay Di®erential EquationsOnly 14 pages are availabe for public view
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Abstract
Delay differential equations (DDEs) are a class of differential equations that have received considerable recent attention and been shown to model many real life problems, traditionally formulated as systems of ordinary differential equations (ODEs), more naturally and more accurately. By the development and progress of science in the recent period another images emerged from these equations, such as:
neutral delay differential equations (NDDEs), Volterra delay-integro-differential equations (VDIDEs), and neutral Volterra delay-integro-differential equations (NVDIDEs). As a result of the difficulty of finding analytical solutions to these equations we often resort to numerical methods to solve these problems. The spline collocation methods, that depend on the second and higher derivatives, for solving DDEs have been considered by several authors. These methods produce less accurate approximations when the solution of these equations has a discontinuity in the second and higher derivatives.
The aim of this thesis is to present a class of spline collocation methods which are based on the first derivative for the numerical solution of DDEs, NDDEs and VDIDEs. When the solution of these equations has a discontinuity in the second and higher derivatives, the present methods produce numerical solutions better than those computed by the previous methods. We present a combination of these methods
and El-Gendi method for the numerical solution of VDIDEs and NVDIDEs. Also, we apply these methods to solve the delay logistic models and delay model for the blood cell population. These methods are also compared with some alternative approaches in terms of estimation precision. These methods are also compared with some alternative approaches in terms of estimation precision. This thesis consists of five chapters as follows:
Chapter 1 is devoted for stating most of the basic concepts in spline functions, collocation methods, and El-Gendi method. We present a brief history and explain the development of delay differential equations and their applications in various fields.
Chapter 2 contains a difference scheme based on C1-splines that is derived for the numerical solution of DDEs. Convergence results show that the methods have a convergence of order six.