Journal
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
Volume 176, Issue 1, Pages 203-214Publisher
ELSEVIER SCIENCE BV
DOI: 10.1016/j.cam.2004.07.013
Keywords
third-order two-point boundary value problem; shooting; automatic differentation; recursive evaluation of Taylor coefficients
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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. (C) 2004 Elsevier B.V. All rights reserved.
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