Discrete Adomian Decomposition solution of Nonlinear Fredholm Integral Equation

In recent papers the solution of Linear and Nonlinear Fredholm Integral Equations was introduced using the Adomian Decomposition Method (ADM). For cases that evaluation of integrals analytically are impossible the decomposition method can not be applied. In this paper a discretized version of the Adomian Decomposition Method is introduced and this method is called Discrete Adomian Decomposition Method (DADM). DADM arises when the quadrature rules are used to approximate the definite integrals which can not be computed analytically. The DADM gives the numerical solution at nodes used in the quadrature rules.