Computational methods for solving the steady flow of a third grade fluid in a porous half space

An important class of fluids commonly used in industries is non-Newtonian fluids. In this paper, two numerical techniques based on rational Legendre functions and Chebyshev polynomials are presented for solving the flow of a third-grade fluid in a porous half space. This problem can be reduced to a nonlinear two-point boundary value problem on semi-infinite interval. Our methods are utilized to reduce the computation of this problem to some algebraic equations. The comparison of the results with the other methods and residual norm show very good accuracy and rate of convergence of our approach.