Rational Bernstein Collocation Method for Solving the Steady Flow of a Third Grade Fluid in a Porous Half Space

Abstract

In the current work, a mathematical model which describes the steady flow of a third grade fluid in a porous half space
is investigated numerically. An approximate expression for solution of the governing non-linear two point boundary value problem on semi-infinite domain is developed as a combination of rational Bernstein functions. A spectral collocation method based on the rational Bernstein functions is introduced and implemented to find numerical solution of the governing problem. The efficiency and accuracy of the proposed numerical technique is illustrated through the figures and tables. The effects of variations of various embedded parameters on the fluid velocity profile have been investigated graphically.