Solution of Third Grade Thin Film Flow Using Algorithmic Differentiation
Abstract
We solve the steady thin film flow problem for a third grade fluid by using Taylor series and shooting. Neither finite difference formulas nor lengthy analytical expressions are used for calculating the derivatives needed. Instead, exact derivatives are computed directly through algorithmic differentiation, which leads to recursive formulas for the derivatives. The method avoids round-off effects and the use of symbolic manipulation systems. Therefore, the method requires much less computational effort when compared to other existing methods for producing results of comparable accuracy. Our numerical results are in excellent agreement with the several approximate solutions obtained previously.
This paper has been withdrawn.