On the use of Hadamard expansions in hyperasymptotic evaluation of Laplace-type integrals—III: Clusters of saddle points
نویسنده
چکیده
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. Themodification to this procedure that is requiredwhen 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. © 2006 Elsevier B.V. All rights reserved. MSC: 30E15; 30E20; 41A60
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تاریخ انتشار 2007