The ``phase function method to solve second-order asymptotically polynomial differential equations

DOI10.1007/s00211-011-0441-9zbMath1256.65080OpenAlexW2087779067MaRDI QIDQ443850

Marco Vianello, Renato Spigler

Publication date: 13 August 2012

Published in: Numerische Mathematik (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00211-011-0441-9

zbMATH Keywords

numerical examplesphase functionshighly oscillatory problemsAiry problemsLiouville-Green asymptotic theoryzeros of the solutions

Mathematics Subject Classification ID

Explicit solutions, first integrals of ordinary differential equations (34A05) Numerical methods for ordinary differential equations (65L99)

Related Items

On the existence of nonoscillatory phase functions for second order ordinary differential equations in the high-frequency regime ⋮ 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 ⋮ On the numerical solution of second order ordinary differential equations in the high-frequency regime ⋮ 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 ⋮ On the asymptotics of Bessel functions in the Fresnel regime ⋮ Improved estimates for nonoscillatory phase functions

Uses Software

• Mathematica

Cites Work

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