Hyperasymptotic evaluation of the Pearcey integral via Hadamard expansions

Richard B. Paris, D. Kaminski

Research output: Contribution to journalArticle

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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.
Original languageEnglish
Pages (from-to)437-452
Number of pages16
JournalJournal of Computational and Applied Mathematics
Volume190
Issue number1-2
DOIs
StatePublished - Jun 2006

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Coalescence
Saddle
Stokes
Numerical results
Curve
Evaluation

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Paris, Richard B.; Kaminski, D. / Hyperasymptotic evaluation of the Pearcey integral via Hadamard expansions.

In: Journal of Computational and Applied Mathematics, Vol. 190, No. 1-2, 06.2006, p. 437-452.

Research output: Contribution to journalArticle

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Hyperasymptotic evaluation of the Pearcey integral via Hadamard expansions. / Paris, Richard B.; Kaminski, D.

In: Journal of Computational and Applied Mathematics, Vol. 190, No. 1-2, 06.2006, p. 437-452.

Research output: Contribution to journalArticle

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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.

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