الفهرس 
INTRODUCTIONOnly 14 pages are availabe for public view
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Abstract
Many of problems lacing physicists engineers and applied mathematicians involve such difficulties to obtain exact solutions such as is nonlinear equations . boundary value problems , difference and differential- difference equations . Consequently , approximate solutions was applied either using numerical or analytical techniques . 1 his thesis is only concerned with analytic techniques in the form of systematic methods of perturbations ( asymptotic expansions ) in terms of a small parameter i:. So the aim in this thesis is to obtain , as much as possible , an accurate approximate solution to some problems that preclude solving them exactly . Consequently , we start to describe the perturbation technique on some simple ordinary algebraic equations having small parameter i: that can be solved exactly in order to make comparisons . Then we progress to linear and nonlinear ordinary differential equations , where different perturbation techniques were applied on them like ihe straightforward expansion , the Lindsteadt’s Poincare’ technique , the Coordinate perturbation technique and the multiple time scales method . Then we show how accurate the solution was during its graphical presentation with the exact solution . A boundary value problem is then solved by a method called the matched asymptotic expansion . This method is used when the small parameter multiplies the highest derivative of the differential equation . Then a composite asymptotic expansion is obtained and represented graphically with the exact solution . But due to obtaining a high accurate composite solution , the difference between it and its exact solution is not visually observed . Hence the relative error is used in order to detect the error that is very small . The application of the perturbation techniques is demonstrated by presenting the details of the work done by Lange and Miura [ 14 ] that describes a biological problem and was analyzed as a boundary’ value problem for singular perturbed linear second order differential - difference equation . A Fuzzy approach to perturbation analysis is partly reviewed as in [29 ]. Finally , Mathematica programs are designed to handle perturbation analysis for classes of linear and nonlinear ordinary differential equations .