Solution of Third Grade Thin Film Flow Using Algorithmic Differentiation
Document Type
Article
Publication Date
6-1-2020
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.
Publication Title
International Journal of Applied and Computational Mathematics
Volume
6
Issue
3
Digital Object Identifier (DOI)
10.1007/s40819-020-00826-1
ISSN
23495103
E-ISSN
21995796
Citation Information
Asaithambi, A. Solution of Third Grade Thin Film Flow Using Algorithmic Differentiation. Int. J. Appl. Comput. Math 6, 74 (2020). https://doi.org/10.1007/s40819-020-00826-1