Mathematics and Computer Applications - Sciene

The main theme of this work is to introduce the general form and fundamental concepts in ordinary and partial delay-differential equations with variable delays and then to find the variational formulation of
delay-differential equations with variable delays in both cases, ordinary and partial and to provide the rules of minimizing the obtained functional in the subject of calculus of variation. Finally, to minimize the

This thesis have three main objectives. The first objective is to give a study of stochastic calculus, including the basic definitions and fundamental concepts related to this topic including the proof of some
results, and among such results is the proof of Hölder's inequality of expectation, the existence and uniqueness theorem of stochastic differential equations and the Euler's method for solving stochastic

 
The main purpose of this work may be divided into the following aspects:
1. Study the Chebyshev polynomials of the first and second kinds defined on the intervals [0,1] and [-1,1] and modify some of their properties

2. Use two methods to solve the linear ordinary differential equations with nonconstant coefficients, namely,Chebyshev-matrix method and Chebyshev series method.
3. Devote Chebyshev series method to solve system of linear Fredholm integral
equations and integro-differential equations.