An optimal homotopy asymptotic method applied to the nonlinear thin film flow problems

Abstract

Purpose

This paper aims to discuss the approximate solution of the nonlinear thin film flow problems. A new analytic approximate technique for addressing nonlinear problems, namely, the optimal homotopy asymptotic method (OHAM), is proposed and used in an application to the nonlinear thin film flow problems.

Design/methodology/approach

This approach does not depend upon any small/large parameters. This method provides a convenient way to control the convergence of approximation series and to adjust convergence regions when necessary.

Findings

The obtained solutions show that the OHAM is more effective, simpler and easier than other methods. The results reveal that the method is explicit. By applying the method to nonlinear thin film flow problems, it was found to be simpler in applicability, and more convenient to control convergence. Therefore, the method shows its validity and great potential for the solution of nonlinear problems in science and engineering.

Originality/value

The proposed method is tested upon nonlinear thin film flow equation from the literature and the results are compared with the available approximate solutions including Adomian decomposition method (ADM), homotopy perturbation method, modified homotopy perturbation method and HAM. Moreover, the exact solution is compared with the available numerical solutions. The graphical representation of the solution is given by Maple and is physically interpreted.

Citation

Manafian, J. and Teymuri sindi, C. (2018), "An optimal homotopy asymptotic method applied to the nonlinear thin film flow problems", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 28 No. 12, pp. 2816-2841. https://doi.org/10.1108/HFF-08-2017-0300