Comparison of optimal homotopy asymptotic method and homotopy perturbation method for strongly non-linear equation

Abstract

In this paper, we employ an approximate analytical method, namely the optimal homotopy asymptotic method (OHAM), to investigate a thin film flow of a third grade fluid down an inclined plane and provided accurate solution unlike other erroneous results available in the literature. The variation of the velocity field for different parameters is compared with the numerical values obtained by the Runge–Kutta Fehlberg fourth–fifth order numerical method and with the homotopy perturbation method (HPM). Finally, it was found that for all values of parameters OHAM agrees well with the numerical disparate HPM.