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

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 m...

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Bibliographic Details
Published in:Journal of computational and applied mathematics 2005-04, Vol.176 (1), p.203-214
Main Author: Asaithambi, Asai
Format: Article
Language:English
Subjects:
Automatic differentation
Exact sciences and technology
Mathematical analysis
Mathematics
Numerical analysis
Numerical analysis. Scientific computation
Partial differential equations
Partial differential equations, boundary value problems
Recursive evaluation of Taylor coefficients
Sciences and techniques of general use
Shooting
Third-order two-point boundary value problem
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Summary: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.
ISSN:0377-0427
1879-1778
DOI:10.1016/j.cam.2004.07.013