Some computational convergent iterative algorithms to solve nonlinear problems

In this article, we apply Fourier transform to convert a nonlinear problem to a suitable equation and then we introduce a modified homotopy perturbation to divide the above equation into some smaller and easier equations. These equations can be solved by some iterative algorithms which are constructed by modified homotopy perturbation and Adomian polynomials. As an example, we use the iterative algorithms to find the exact solution of nonlinear ordinary and partial differential equations (in abbreviated form, ODE and PDE). To show ability and validity of the presented algorithms, we solve Korteweg-de Vries (KdV) equation to approximate the exact solution with a high accuracy. Furthermore, a discussion is presented herein about the convergence of the proposed algorithms in Banach space