Daftardar-Jafari method for solving nonlinear thin film flow problem

Abstract

The aim of this paper is to develop the Daftardar-Jafari iterative method (DJM) for a mathematical model that represents the nonlinear thin film flow of a non-Newtonian third-grade fluid on a moving belt with the aim to obtain an approximate solution of high accuracy. When applying the DJM there is no need to resort to any additional techniques such as evaluating Adomian’s polynomials as in the Adomian decomposition method (ADM) or such as using Lagrange multipliers in the variational iteration method (VIM). The accuracy of our results is numerically verified by evaluating the functions of the error remainder and the maximal error remainders. In addition, these results are analyzed by comparing the accuracy of the DJM solutions with those of the fourth order Runge-Kutta method (RKM), ADM and VIM at the same parameter values. All the evaluations have been successfully performed in an iterative way by using the symbolic manipulator Mathematica®.