On the use of Hadamard expansions in hyperasymptotic evaluation of Laplace-type integrals-III: Clusters of saddle points

Authors:
R. B. Paris
Affiliations:
Division of Mathematical Sciences, University of Abertay Dundee, Dundee DD1 1HG, UK
Venue:
Journal of Computational and Applied Mathematics
Year:
2007

Citing 3
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On the use of Hadamard expansions in hyperasymptotic evaluation of Laplace-type integrals: II. complex variable

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Hyperasymptotic evaluation of the Pearcey integral via Hadamard expansions

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On the use of Hadamard expansions in hyperasymptotic evaluation of Laplace-type integrals-IV: Poles

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Abstract

It is shown how the recently developed Hadamard expansion procedure can be applied to the hyperasymptotic evaluation of Laplace-type integrals containing a large variable when the phase function has a cluster of close-lying saddle points. The modification to this procedure that is required when the saddles in the cluster coalesce to form a single higher-order saddle is discussed. An example is also considered in which there is both a coalescence of saddles and a Stokes phenomenon as the phase of the large variable is allowed to vary. Numerical examples are given to illustrate the accuracy that can be obtained with this new procedure.