تفاصيل الرسالة العلمية

In this thesis we used difference equations to find the smallest root for a cubic equation. We generalized the result for fifth order algebraic equations. Also, it is to be mentioned that the new method is valid for equations in which the smallest root is less than the modulus of the complex roots. Finally, we used Adomian decomposition method to find the smallest root for any algebraic equation; the latest method depends on changing the idea of finding the root of a polynomial to a fixed-point problem. For comparison purposes, some numerical examples are given to illustrate the validity of the proposed methods