Title

Solution of Third Grade Thin Film Flow Using Algorithmic Differentiation

Document Type

Article

Publication Date

6-1-2020

Subject Area

ARRAY(0x557a926b5138)

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

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