الفهرس 
Chapter 1 IntroductionOnly 14 pages are availabe for public view
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Abstract
The main purpose of our thesis is to investigate some different classes of ordinary differential equations arising in many applications in engineering. Most of these problems have no analytic solutions so, numerical methods are encountered. We use the collocation spectral method with Laguerre basis to solve these equations. In our work, we compared our results with the analytic solution (if it exists) and with other numerical methods. That comparison declared that Laguerre collocation method is an efficient, accurate and fast technique to solve various types of ordinary differential equations. The thesis is organized as follows: Chapter (1) provides an overview of ordinary differential equations and the numerical methods used to solve them. Also gives a good representation of the equations already solved using Laguerre basis. In Chapter (2), Laguerre collocation technique is presented and applied to high order differential equations with constant and variable delays. Several examples were solved and their results were compared to other methods to emphasize the accuracy and efficiency of Laguerre method. In Chapter (3), Laguerre Matrices for nonlinear terms in differential equations are presented and applied to Troesch’s nonlinear differential equation and the results are compared to those from other different methods. Chapter (4) shows the matrix form of the systems of linear and nonlinear differential equations that arise in numerous applications and the application of the proposed method to solve them. The comparison of results obtained from the proposed method and other methods shows the efficiency of Laguerre collocation method. Chapter (5) contains the conclusion of our work along with suggested future work.