A method for the numerical evaluation of the oscillatory integrals associated with the cuspoid catastrophes: application to Pearcey's integral and its derivatives

DOI10.1088/0305-4470/15/4/021zbMath0485.65019OpenAlexW2017663905MaRDI QIDQ3945478

Peter R. Curtis, J. N. L. Connor

Publication date: 1982

Published in: Journal of Physics A: Mathematical and General (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1088/0305-4470/15/4/021

zbMATH Keywords

oscillatory integralsCauchy's theoremJordan's lemmacuspoid catastrophescuspoid canonical integralsPearcey's integral

Mathematics Subject Classification ID

Numerical quadrature and cubature formulas (65D32) Numerical methods for trigonometric approximation and interpolation (65T40) Conjugate functions, conjugate series, singular integrals (42A50)

Related Items (15)

Hyperasymptotic evaluation of the Pearcey integral via Hadamard expansions ⋮ Theory and numerical evaluation of oddoids and evenoids: oscillatory cuspoid integrals with odd and even polynomial phase functions ⋮ The swallowtail integral in the highly oscillatory region III ⋮ Asymptotic approximation of a highly oscillatory integral with application to the canonical catastrophe integrals ⋮ Contour integral solutions of the parabolic wave equation ⋮ An asymptotic expansion of the hyberbolic umbilic catastrophe integral ⋮ UNIFORMLY ASYMPTOTIC SOLUTIONS FOR PSEUDODIFFERENTIAL EQUATIONS WITH SINGULAR INTEGRAL OPERATORS ⋮ The Pearcey integral in the highly oscillatory region ⋮ Diffraction of pulses in the vicinity of simple caustics and caustic cusps ⋮ The asymptotic expansion of the swallowtail integral in the highly oscillatory region ⋮ Electronic optics in graphene in the semiclassical approximation ⋮ The swallowtail integral in the highly oscillatory region. II ⋮ On the zeros of the Pearcey integral ⋮ Differential equations for the cuspoid canonical integrals ⋮ Convergent and asymptotic expansions of the Pearcey integral

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