Hyperasymptotic evaluation of the Pearcey integral via Hadamard expansions

Richard B. Paris; D. Kaminski

doi:10.1016/j.cam.2005.01.038

Hyperasymptotic evaluation of the Pearcey integral via Hadamard expansions

Richard B. Paris
, D. Kaminski

Research output: Contribution to journal › Article › peer-review

17 Citations (Scopus)

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.

Original language	English
Pages (from-to)	437-452
Number of pages	16
Journal	Journal of Computational and Applied Mathematics
Volume	190
Issue number	1-2
DOIs	https://doi.org/10.1016/j.cam.2005.01.038
Publication status	Published - Jun 2006

Keywords

Pearcey integral
Hyperasymptotics
Hadamard expansions
Caustic curve
Stokes set

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10.1016/j.cam.2005.01.038

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title = "Hyperasymptotic evaluation of the Pearcey integral via Hadamard expansions",

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.",

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AU - Paris, Richard B.

AU - Kaminski, D.

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AB - 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.

U2 - 10.1016/j.cam.2005.01.038

DO - 10.1016/j.cam.2005.01.038

M3 - Article

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VL - 190

SP - 437

EP - 452

JO - Journal of Computational and Applied Mathematics

JF - Journal of Computational and Applied Mathematics

IS - 1-2

ER -

Hyperasymptotic evaluation of the Pearcey integral via Hadamard expansions

Abstract

Keywords

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