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Solution of third grade thin film flow using algorithmic differentiation. (English) Zbl 1446.76072

Summary: 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 several approximate solutions obtained previously.

MSC:

76A20 Thin fluid films
76A05 Non-Newtonian fluids
76M45 Asymptotic methods, singular perturbations applied to problems in fluid mechanics
65D25 Numerical differentiation
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