Numerical evaluation of Airy-type integrals arising in uniform asymptotic analysis

DOI10.1016/j.cam.2020.112717zbMath1493.65045arXiv2001.02097OpenAlexW3000494496MaRDI QIDQ2297158

Javier Segura, Amparo Gil, Nico M. Temme

Publication date: 18 February 2020

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2001.02097

zbMATH Keywords

numerical integrationsaddle point analysisasymptotic approximationsAiry-type integralscomputing special functionsnumerical quadrature of oscillatory integrals

Mathematics Subject Classification ID

Asymptotic approximations, asymptotic expansions (steepest descent, etc.) (41A60) Computation of special functions and constants, construction of tables (65D20) Numerical quadrature and cubature formulas (65D32) Bessel and Airy functions, cylinder functions, ({}_0F_1) (33C10)

Related Items (1)

On numerical approaches to nonlinear Schrödinger and Korteweg-de Vries equations for piecewise smooth and slowly decaying initial data

Uses Software

• DLMF
• Algorithm 822

Cites Work

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• Complex Gaussian quadrature of oscillatory integrals
• Numerical algorithms for uniform Airy-type asymptotic expansions
• An adaptive contour code for the numerical evaluation of the oscillatory cuspoid canonical integrals and their derivatives.
• Computing complex Airy functions by numerical quadrature
• Computation of asymptotic expansions of turning point problems via Cauchy's integral formula: Bessel functions
• The asymptotic expansion of the swallowtail integral in the highly oscillatory region
• On nonoscillating integrals for computing inhomogeneous Airy functions
• The Exponentially Convergent Trapezoidal Rule
• Analytic formulas for the evaluation of the Pearcey integral
• Asymptotic Methods for Integrals
• Computing Highly Oscillatory Integrals
• A Numerical Method for Oscillatory Integrals with Coalescing Saddle Points
• Numerical Methods for Special Functions
• Algorithm 822: GIZ, HIZ

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