As will be seen from the examples below, this reduction in the number of terms of u0 will result in a reduction of the computational work and will accelerate the convergence.Further, this slight variation in the definition of the components u0 and u1 may provide the solution by using two iterations only. Furthermore, the calculations below will show that there is no need sometimes to evaluate the so-called Adomian polynomials required for the nonlinear dierential and integral equations.