On the numerical solution of second order ordinary differential equations in the high-frequency regime

DOI10.1016/j.acha.2016.05.002zbMath1380.65119arXiv1409.6049OpenAlexW2963429571MaRDI QIDQ1690703

James Bremer

Publication date: 12 January 2018

Published in: Applied and Computational Harmonic Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1409.6049

zbMATH Keywords

oscillationnumerical experimentsfast algorithmsspecial functionsphase functionsBessel's equationhigh-frequency regimesecond-order linear ordinary differential equations

Mathematics Subject Classification ID

Linear ordinary differential equations and systems (34A30) Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations (34C10) Numerical methods for initial value problems involving ordinary differential equations (65L05)

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 ⋮ A maximum entropy method for solving the boundary value problem of second order ordinary differential equations ⋮ Fast algorithms for the multi-dimensional Jacobi polynomial transform ⋮ 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 ⋮ 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
• FastGaussQuadrature

Cites Work

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• $\mathcal{O}(1)$ Computation of Legendre Polynomials and Gauss--Legendre Nodes and Weights for Parallel Computing
• Bessel Functions for Large Arguments
• Modern Fourier Analysis
• Fast and Accurate Computation of Gauss--Legendre and Gauss--Jacobi Quadrature Nodes and Weights

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