Hyperasymptotic evaluation of the Pearcey integral via Hadamard expansions

Richard B. Paris, D. Kaminski

    Research output: Contribution to journalArticlepeer-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 languageEnglish
    Pages (from-to)437-452
    Number of pages16
    JournalJournal of Computational and Applied Mathematics
    Volume190
    Issue number1-2
    DOIs
    Publication statusPublished - Jun 2006

    Keywords

    • Pearcey integral
    • Hyperasymptotics
    • Hadamard expansions
    • Caustic curve
    • Stokes set

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