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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

A dispersion analysis for difference schemes: tables of generalized Airy functions


Authors: R. C. Y. Chin and G. W. Hedstrom
Journal: Math. Comp. 32 (1978), 1163-1170
MSC: Primary 65M10
MathSciNet review: 0494982
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Abstract: This paper contains graphs and tables of the function

$\displaystyle A{i_{p,q}}(\alpha ,x) = \int_{ - \infty }^\infty {{{(2\pi )}^{ - 1}}\exp \{ i{y^p}/p - \alpha {y^q}/q + ixy\} \;dy} $

and its indefinite integral for $ p = 3,5,7$, for $ q = 2,4,6$, and for several values of $ \alpha $ with $ \alpha \geqslant 0$. It is shown how these tables should influence the choice of an artificial viscosity for a difference scheme for a linear hyperbolic equation.

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Additional Information

DOI: http://dx.doi.org/10.1090/S0025-5718-1978-0494982-6
PII: S 0025-5718(1978)0494982-6
Article copyright: © Copyright 1978 American Mathematical Society