### Abstract

*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 | |

State | Published - Jun 2006 |

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### Cite this

*Journal of Computational and Applied Mathematics*,

*190*(1-2), 437-452. DOI: 10.1016/j.cam.2005.01.038

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*Journal of Computational and Applied Mathematics*, vol 190, no. 1-2, pp. 437-452. DOI: 10.1016/j.cam.2005.01.038

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

Research output: Contribution to journal › Article

TY - JOUR

T1 - Hyperasymptotic evaluation of the Pearcey integral via Hadamard expansions

AU - Paris,Richard B.

AU - Kaminski,D.

PY - 2006/6

Y1 - 2006/6

N2 - 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.

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

VL - 190

SP - 437

EP - 452

JO - Journal of Computational and Applied Mathematics

T2 - Journal of Computational and Applied Mathematics

JF - Journal of Computational and Applied Mathematics

SN - 0377-0427

IS - 1-2

ER -