Asymptotic-numerical approximations for highly oscillatory second-order differential equations by the phase function method
type: Item
instance of: scholarly article
title: Asymptotic-numerical approximations for highly oscillatory second-order differential equations by the phase function method
zbMATH Open document ID: 1404.65059
author: Renato Spigler
published in: Journal of Mathematical Analysis and Applications
publication date: 2018-04-25T00:00:00Z
Mathematics Subject Classification ID: 65L05
Mathematics Subject Classification ID: 65L10
Mathematics Subject Classification ID: 34B05
Mathematics Subject Classification ID: 34A30
Mathematics Subject Classification ID: 34C10
zbMATH DE Number: 6864735
zbMATH Keywords: phase function method
zbMATH Keywords: highly oscillatory differential equations
zbMATH Keywords: Liouville-Green (WKB) approximation
zbMATH Keywords: Boruvka's theory of linear differential transformations
zbMATH Keywords: asymptotic-numerical approximation of zeros
zbMATH Keywords: forced oscillations
MaRDI profile type: Publication
full work available at URL: j.jmaa.2018.03.027
OpenAlex ID: W2793354687
cites work: Q5558293
cites work: Q5549974
cites work: Q5627047
cites work: On the numerical solution of second order ordinary differential equations in the high-frequency regime
cites work: On the Numerical Calculation of the Roots of Special Functions Satisfying Second Order Ordinary Differential Equations
cites work: Improved estimates for nonoscillatory phase functions
cites work: On numerical methods for highly oscillatory problems in circuit simulation
cites work: On highly oscillatory problems arising in electronic engineering
cites work: On second-order differential equations with highly oscillatory forcing terms
cites work: A new numerical method for the integration of highly oscillatory second-order ordinary differential equations
cites work: Computing the Zeros and Turning Points of Solutions of Second Order Homogeneous Linear ODEs
cites work: A combined symbolic and numerical algorithm for the computation of zeros of orthogonal polynomials and special functions
cites work: A Fast Algorithm for the Calculation of the Roots of Special Functions
cites work: Q5330830
cites work: On the existence of nonoscillatory phase functions for second order ordinary differential equations in the high-frequency regime
cites work: On the asymptotics of Bessel functions in the Fresnel regime
cites work: A Gautschi-type method for oscillatory second-order differential equations
cites work: On the global error of discretization methods for highly-oscillatory ordinary differential equations
cites work: Think globally, act locally: Solving highly-oscillatory ordinary differential equations
cites work: Q5710743
cites work: Q4002326
cites work: NIST digital library of mathematical functions
cites work: Q3126395
cites work: Q4356577
cites work: The Zeros of Special Functions from a Fixed Point Method
cites work: A Numerical Method for Evaluating Zeros of Solutions of Second-Order Linear Differential Equations
cites work: Global existence and uniqueness for the Kummer transformation problem subject to non-Cauchy data
cites work: The ``phase function'' method to solve second-order asymptotically polynomial differential equations
DOI: 10.1016/J.JMAA.2018.03.027
describes a project that uses: Digital Library of Mathematical Functions
description: scientific article; zbMATH DE number 6864735