Solution of the Falkner-Skan equation by recursive evaluation of Taylor coefficients

Authors:
Asai Asaithambi
Affiliations:
Department of Computer Science, Parks College of Engineering and Aviation, Saint Louis University, 3450 Lindell Blvd., St. Louis, MO 63103, USA
Venue:
Journal of Computational and Applied Mathematics
Year:
2005

Citing 2
Cited 0

A finite-difference method for the Falkner-Skan equation

Applied Mathematics and Computation
Methods and Applications of Interval Analysis (SIAM Studies in Applied and Numerical Mathematics) (Siam Studies in Applied Mathematics, 2.)

Methods and Applications of Interval Analysis (SIAM Studies in Applied and Numerical Mathematics) (Siam Studies in Applied Mathematics, 2.)

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Abstract

We present a computational method for the solution of the third-order boundary value problem characterized by the well-known Falkner-Skan equation on a semi-infinite domain. Numerical treatments of this problem reported in the literature thus far are based on shooting and finite differences. While maintaining the simplicity of the shooting approach, the method presented in this paper uses a technique known as automatic differentiation, which is neither numerical nor symbolic. Using automatic differentiation, a Taylor series solution is constructed for the initial value problems by calculating the Taylor coefficients recursively. The effectiveness of the method is illustrated by applying it successfully to various instances of the Falkner-Skan equation.