Abstract
Integral equation has been one of the essential tools for various areas of applied mathematics. The Fredholm integral equations can be derived from boundary value problems. In this paper, we are concerned with the application of the Adomian Decomposition Method by using MATLAB program for the Fredholm integral equation of the second kind. The new computational algorithm is applied directly without using any transformation, linearization, discretization or taking some restrictive assumptions. An exact solution of the illustrative example was successfully fund using the proposed method, and the results are compared with the results of the existing methods. The Adomain Decomposition will be obtained easily without linearizing the problem by implementing the Adomain Decomposition Method by using MATLAB program rather than the standard methods for the exact solutions. The concern will be on the determination of the solution y (x) of the Fredholm integral equations of the second kind. The results indicated that the method is very effective and simple.