Convergent and asymptotic expansions of solutions of second-order differential equations with a large parameter

DOI10.1142/S0219530514500328zbMath1300.34028OpenAlexW1997673024MaRDI QIDQ2925313

Ester Pérez Sinusía, Chelo Ferreira, José Luis López

Publication date: 21 October 2014

Published in: Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s0219530514500328

zbMATH Keywords

singular pointsGreen's functionssecond-order differential equationsasymptotic expansionsturning pointsBessel functionsVolterra integral equations of the second kindfixed-point theorems

Mathematics Subject Classification ID

Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations (34A12) Asymptotic approximations, asymptotic expansions (steepest descent, etc.) (41A60) Analytical theory of ordinary differential equations: series, transformations, transforms, operational calculus, etc. (34A25) Green's functions for ordinary differential equations (34B27) Series expansions (e.g., Taylor, Lidstone series, but not Fourier series) (41A58)

Related Items (3)

Existence and uniqueness of exact WKB solutions for second-order singularly perturbed linear ODEs ⋮ ASYMPTOTIC AND CONVERGENT EXPANSIONS FOR SOLUTIONS OF THIRD-ORDER LINEAR DIFFERENTIAL EQUATIONS WITH A LARGE PARAMETER ⋮ Convergent and asymptotic methods for second-order difference equations with a large parameter

Cites Work

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• Olver's asymptotic method revisited; case I
• Approximation of the Jacobi polynomials and the Racah coefficients
• Singular perturbation potentials
• On the approximation of the Jacobi polynomials
• 𝓟𝓣-symmetric quantum mechanics
• Convergent Expansions for Solutions of Linear Ordinary Differential Equations Having a Simple Turning Point, with an Application to Bessel Functions
• Spiked harmonic oscillators

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