الفهرس 
Chapter 1 Genocchi PolynomialsOnly 14 pages are availabe for public view
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Abstract
Differential equations have a very important position in mathematics, combining the best of pure mathematics with some of the most significant models in different branches of science, engineering, and mathematics with their ability to provide more realistic simulations to both classical and modern real life phenomenons. Differential equations have two types, which are ordinary and partial differential equations. The evaluating of analytical solution for ordinary and partial differential equations is very hard and difficult, so scientists are trying to provide numerical techniques for solving this type of equations. one of the most famous and important methods of numerical methods for solving differential equations are collocation methods. There are many different polynomials using by collocation methods. In this thesis, we deal with Genocchi polynomials, which are orthogonal polynomials and the interval of work for them is [0, 1]. We employed Genocchi basis to four kinds of ordinary differential equations, which are higher order differential equations, The Bratu equation, The Troesch equation, and fractional differential boundary value problems. The first chapter serves as an introduction, literature review, introducing the fundamentals of Genocchi basis, and the differentiation matrices for differential equations. In chapter two, the Genocchi collocation method is used to solve higher order boundary value problems of both linear and nonlinear cases. The Bratu and Troesch equations are approximated using the Genocchi collocation method in chapter three. In addition, fractional boundary value problems are discussed in chapter four, with the Genocchi collocation method being used to get an approximate solution.