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Efficient and accurate computation of the incomplete Airy functionsThe incomplete Airy integrals serve as canonical functions for the uniform ray optical solutions to several high-frequency scattering and diffraction problems that involve a class of integrals characterized by two stationary points that are arbitrarily close to one another or to an integration endpoint. Integrals with such analytical properties describe transition region phenomena associated with composite shadow boundaries. An efficient and accurate method for computing the incomplete Airy functions would make the solutions to such problems useful for engineering purposes. In this paper a convergent series solution for the incomplete Airy functions is derived. Asymptotic expansions involving several terms are also developed and serve as large argument approximations. The combination of the series solution with the asymptotic formulae provides for an efficient and accurate computation of the incomplete Airy functions. Validation of accuracy is accomplished using direct numerical integration data.
Document ID
19930071154
Acquisition Source
Legacy CDMS
Document Type
Reprint (Version printed in journal)
Authors
Constantinides, E. D.
(NASA Langley Research Center Hampton, VA, United States)
Marhefka, R. J.
(Ohio State Univ. Columbus, United States)
Date Acquired
August 16, 2013
Publication Date
August 1, 1993
Publication Information
Publication: Radio Science
Volume: 28
Issue: 4
ISSN: 0048-6604
Subject Category
Numerical Analysis
Accession Number
93A55151
Funding Number(s)
CONTRACT_GRANT: NSG-1498
Distribution Limits
Public
Copyright
Other

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