Development of the Banach contraction method for the solution of nonlinear thin film flows of non-Newtonian fluids

Abstract

The aim of this study is to present a new implementation of an efficient iterative method proposed by Daftardar-Gejji and Bhalekar to solve a nonlinear initial value problem. We consider the thin film problem of a non-Newtonian fluid on a moving belt. The proposed method is based on using the Banach’s contraction principle. In order to determine the accuracy of the obtained approximate solutions, several comparisons were done against solutions obtained by other authors using the Runge–Kutta method as well as the Newton–Raphson–Euler-based solution. Comparisons with the variational iteration method and the homotopy perturbation method were also made. Several measures have been adopted to provide the error analysis for the derived approximate solution: the error remainder with the maximal error remainder, the second norm and the root mean squared norm. The application of the proposed technique shows the purpose of the obtained approximate solution where no additional assumptions are needed for the nonlinear terms. Calculations were performed using the computer algebra system MATHEMATICA®10.