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

In this paper, we decide to compare rational and exponential Legendre functions Tau approach to solve the governing equations for the flowof 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.