A semi-analytical iterative method for solving nonlinear thin film flow problems

This paper presents a new implementation of a reliable iterative method proposed by Temimi and Ansari namely (TAM) for approximate solutions of a nonlinear problem that arises in the thin film flow of a third grade fluid on a moving belt. The solution is obtained in the form of a series that converges to the exact solution with easily computed components, without any restrictive assumptions for nonlinear terms. The results are bench-marked against a numerical solution based on the classical Runge-Kutta method (RK4) and an excellent agreement is observed. Error analysis of the approximate solution is performed using the error remainder and the maximal error remainder. An exponential rate for the convergence is achieved. A symbolic manipulator Mathematica ®10 was used to evaluate terms in the iterative process.