Rational and Exponential Legendre Tau Method on Steady Flow of a Third Grade Fluid in a Porous Half Space

Abstract

In this paper, we decide to compare rational and exponential Legendre functions Tau approach to solve the governing equations for the flow of a third grade fluid in a porous half space. Firstly, we estimate an upper bound for function approximation based on mentioned functions in semi-infinite domain, and discuss that the analytical functions have a superlinear convergence for these basis. Also the operational matrices of derivative and product of these functions are presented to reduce the solution of this problem to the solution of a system of nonlinear algebraic equations. The comparison of the results of rational and exponential Legendre Tau methods with numerical solution shows the efficiency and accuracy of these methods. We also make a comparison between these two methods themselves and show that using exponential functions, leads to more accurate results and faster convergence in this problem.