Improved estimates for nonoscillatory phase functions

DOI10.3934/dcds.2016.36.4101zbMath1343.34034arXiv1505.05548OpenAlexW2963336863MaRDI QIDQ262081

Vladimir Rokhlin, James Bremer

Publication date: 29 March 2016

Published in: Discrete and Continuous Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1505.05548

zbMATH Keywords

ordinary differential equationsasymptotic expansionsspecial functionsBessel functionsphase functions

Mathematics Subject Classification ID

Linear ordinary differential equations and systems (34A30) Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type (42A38) Asymptotic properties of solutions to ordinary differential equations (34D05)

Related Items (10)

An algorithm for the rapid numerical evaluation of Bessel functions of real orders and arguments ⋮ An algorithm for the numerical evaluation of the associated Legendre functions that runs in time independent of degree and order ⋮ Quasi-analytical root-finding for non-polynomial functions ⋮ Phase function methods for second order linear ordinary differential equations with turning points ⋮ On the Numerical Calculation of the Roots of Special Functions Satisfying Second Order Ordinary Differential Equations ⋮ An Adaptive Spectral Method for Oscillatory Second-Order Linear ODEs with Frequency-Independent Cost ⋮ Phase function methods for second order inhomogeneous linear ordinary differential equations ⋮ On the nonoscillatory phase function for Legendre's differential equation ⋮ Asymptotic-numerical approximations for highly oscillatory second-order differential equations by the phase function method ⋮ A quasilinear complexity algorithm for the numerical simulation of scattering from a two-dimensional radially symmetric potential

Uses Software

• DLMF

Cites Work

• On the existence of nonoscillatory phase functions for second order ordinary differential equations in the high-frequency regime
• The ``phase function method to solve second-order asymptotically polynomial differential equations
• Bounds for ratios of modified Bessel functions and associated Turán-type inequalities
• Hyperasymptotic solutions of second-order linear differential equations. I
• Hyperasymptotic solutions of second-order linear differential equations. II
• On the asymptotics of Bessel functions in the Fresnel regime
• Bessel Functions for Large Arguments
• Modern Fourier Analysis
• Classical Fourier Analysis
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