On the existence of nonoscillatory phase functions for second order ordinary differential equations in the high-frequency regime

DOI10.1016/j.jcp.2015.02.028zbMath1349.34037arXiv1409.4381OpenAlexW2043629264MaRDI QIDQ349765

Vladimir Rokhlin, James Bremer, Zhu Heitman

Publication date: 5 December 2016

Published in: Journal of Computational Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1409.4381

zbMATH Keywords

ordinary differential equationsspecial functionsphase functions

Mathematics Subject Classification ID

Analytical theory of ordinary differential equations: series, transformations, transforms, operational calculus, etc. (34A25) Other functions coming from differential, difference and integral equations (33E30) Numerical approximation and evaluation of special functions (33F05) Numerical methods for ordinary differential equations (65L99)

Related Items (9)

A new type of sharp bounds for ratios of modified Bessel functions ⋮ Fast algorithms for the multi-dimensional Jacobi polynomial transform ⋮ On the Numerical Calculation of the Roots of Special Functions Satisfying Second Order Ordinary Differential Equations ⋮ On the numerical solution of second order ordinary differential equations in the high-frequency regime ⋮ An Adaptive Spectral Method for Oscillatory Second-Order Linear ODEs with Frequency-Independent Cost ⋮ On the nonoscillatory phase function for Legendre's differential equation ⋮ A hierarchical butterfly LU preconditioner for two-dimensional electromagnetic scattering problems involving open surfaces ⋮ Asymptotic-numerical approximations for highly oscillatory second-order differential equations by the phase function method ⋮ Improved estimates for nonoscillatory phase functions

Uses Software

• DLMF

Cites Work

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• The ``phase function method to solve second-order asymptotically polynomial differential equations
• Bounds for ratios of modified Bessel functions and associated Turán-type inequalities
• On the Lambert \(w\) function
• On the asymptotics of Bessel functions in the Fresnel regime
• Bessel Functions for Large Arguments
• Modern Fourier Analysis
• A Numerical Method for Evaluating Zeros of Solutions of Second-Order Linear Differential Equations

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