Hyperasymptotic evaluation of the Pearcey integral via Hadamard expansions

Authors:
R. B. Paris;D. Kaminski
Affiliations:
Division of Mathematical Sciences, University of Abertay Dundee, Dundee, UK;Department of Mathematics & Computer Science, University of Lethbridge, Lethbridge, Alberta, Canada
Venue:
Journal of Computational and Applied Mathematics - Special issue: International conference on mathematics and its application
Year:
2006

Citing 4
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Abstract

We describe high-precision computations of the Pearcey integral Pe(x, y) for real x and y by means of Hadamard expansions. Numerical results for (x, y) situated in different regions of the x, y-plane are given to illustrate the levels of precision that can be achieved. Particular emphasis is given to computation in the neighbourhood of the two cusped curves associated with Pe(x, y) across which there is either a coalescence of saddles or a Stokes phenomenon.