A comparison between Newton’s method and A.D.M.for solving especial Fredholm integral Equations

The aim of this paper is to comparison between Newton’s Method and Adomian decomposition method (A.D.M) to solve especial kinds of nonlinear of Fredholm integral equations. The study follows three steps: First we apply Newton’s method and address theoretical results on existence and uniqueness of the solution. Then main structure of A.D.M, we can used this method to solve Fredholm integral equations of the second kind will be discussed. Finally, numerical example is prepared to illustrate these considerations. The method can be applied to nonitegrable equations as well as to integrable ones