الفهرس 
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Abstract
In this thesis three chapters, chapter I consists of five sections: 1- Introduction. 2- Some definitions. 3- Gradient method. 4- Application of the gradient method. 5- Solution of ordinary differential equations involving differential operators of order 2N., chapter II {Solution of ordinary differential equations with polynomial coefficients}. & chapter III {Spline functions and gradient method} consists of four sections: 1- Introduction. 2- Some definitions. 3- Best approximation. 4- Solution of ordinary differential equations by using the spline functions.