A numerical method based on rational Gegenbauer functions for solving boundary layer flow of a Powell–Eyring non-Newtonian fluid

In this paper, the boundary layer flow of a Powell–Eyring non-Newtonian fluid over a stretching sheet is considered which is lucrative in the production of many beneficial materials in the industry. Rational Gegenbauer (RG) functions are used to find the better solution comparing to other current works. The drawback of nonlinearity is met using a linearization method, namely, the quasi-linearization method (QLM). As comping on a semi-infinite domain, an approximation is considered to satisfy the infinity condition using the algebraic mapping of ξ-Lξ+L\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\frac{\xi -L}{\xi +L}$$\end{document}, where L is a positive arbitrary numerical parameter and a suitable value is calculated for it. Using the QLM, the equation is converted into a sequence of linear ordinary differential equations (ODE); then, these ODEs are solved using the RG collocation method. Finally, the numerical results are presented and the proposed method is compared with the state-of-the-art methods.