الفهرس 
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Abstract
The primary purpose of the thesis is to present efficient numerical schemes using different bases functions for the solution of ordinary and partial differential equations with nonlocal boundary conditions. Numerical results and comparisons showed excellent agreement with results of problems which have analytic solution or with those obtained using other approximation methods. The thesis is organized as follows: In chapter one, an overview of ordinary and partial differential equation, their applications and solution methods are presented, in addition, thesis outline and work objectives are introduced. In chapter two, sinc-collocation method and Bernstein-collocation is developed for SturmLiouville problems with nonlocal integral boundary conditions. The sinc collocation approach for solving a parabolic PDE with nonlocal in chapter three. The Legendre collocation for solving Bagley-Torvik equation is considered in chapter four.In chapter five,Chelyshkov operational matrix approach for solving Bagley-Torvik equation method Comparisons with other methods in literature proved the accuracy of the proposed scheme. Concluding remarks and suggested future work are given in chapter six.