الفهرس 
Adomian decomposition methodOnly 14 pages are availabe for public view
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Abstract
Diferential equations is a mathematical equation that relates some function with its deriv- atives. In applications, the functions usually represent physical quantities, the derivatives represent their rates of change, and the equation de nes a relationship between the two .It plays a prominent role in di¤erent engineering branches from modeling engineering structures, describing important phenomena, to simulating the numerical behavior of engineering dynamic systems. They can be used as powerful numerical tools to model a variety of engineering systems. Because of the importance of the di¤erential equations in many engineering disciplines, a number of analytical and numerical methods have been proposed to accurately solve for vari-ous linear and nonlinear di¤erential equations. For example, Adomian decomposition method (ADM), one of the most popular methods, which enables the accurate and e¢ cient analytic solution of linear or nonlinear ordinary or partial di¤erential equations. This technique is based on the representation of a solution to a functional equation as series of functions. Each term of the series is obtained from a polynomial generated by a power series expansion of an analytic function. Although the formulation of the Adomian method is very simple, the calculations of the polynomials and the veri cation of convergence of the function series in speci c situations are usually a di¢ cult task. We illustrate the e¢ ciency of the technique for several speci c examples which compared with the exact solution While you may not be able to nd the exact answer, you can nd an approximate answer and the more computer time, the closer that approximation will be to the correct answer. A trick that lets you get closer and closer to an exact answer is a numerical method. Numerical methods nd solutions close to the answer without ever knowing what that answer is. As such, an important part of every numerical method is a proof that it works. So that we need numerical methods because a lot of problems are not analytically solvable with a proof that it works. In a system of ordinary di¤erential equations there can be any number of unknown functions yi, but all of these functions must depend on a single ”independent variable” x, which is the same for each function. Partial di¤erential equations involve two or more independent variables. In this thesis, many theories have been appeared to the Adomian decomposition method. The process of selecting the appropriate inverse operator for a given problem gives the more accurate solution. The objective of this work is to study the approximate solution of some classes of nonlinear BVP using ADM and the thesis is divided into four chapters. First chapter: introduce the description of the method with applications from real life and engineering applications with explanation of advantages and disadvantages. Second chapter: Display linear and nonlinear ordinary di¤erential equations where this work show the development occurs. Third chapter: How to apply ADM to linear and nonlinear partial di¤erential equations to real life problems; Find more accurate solution to life and engineering problems. Forth chapter: introduce a new continuous solution of solving a class of nonlinear two point boundary value problem using ADM.