WKB (Liouville-Green) analysis of second order difference equations and applications
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Publication:1196885
DOI10.1016/0021-9045(92)90003-7zbMath0764.41030OpenAlexW2087930911MaRDI QIDQ1196885
Dale T. Smith, Jeffrey S. Geronimo
Publication date: 16 January 1993
Published in: Journal of Approximation Theory (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/0021-9045(92)90003-7
Asymptotic approximations, asymptotic expansions (steepest descent, etc.) (41A60) Numerical methods for initial value problems involving ordinary differential equations (65L05) Additive difference equations (39A10)
Related Items (16)
Asymptotic analysis of solutions in the ``double root case ⋮ Dichotomy of WKB-solutions of discrete Schrödinger equation ⋮ Canonical forms and discrete Liouville-Green asymptotics for second-order linear difference equations ⋮ Asymptotic expansion of orthogonal polynomials via difference equations ⋮ Corrigendum to ``WKB (Liouville-Green) analysis of second order difference equations and applications [J. Approx. Theory 69 (1992) 269-301] ⋮ Energy splitting in dynamical tunneling ⋮ WKB estimates for \(2\times 2\) linear dynamic systems on time scales ⋮ Convergent and asymptotic methods for second-order difference equations with a large parameter ⋮ Asymptotic analysis of the Hermite polynomials from their differential–difference equation ⋮ Asyptotics for linear difference equations I:basic theory ⋮ The spectral transform in the semiclassical limit of a finite discrete NLS chain ⋮ Monotone Jacobi parameters and non-Szegő weights ⋮ Riccati techniques and approximation for a second-order Poincaré difference equation ⋮ WKB asymptotics of meromorphic solutions to difference equations ⋮ Liouville-Green-Olver approximations for complex difference equations ⋮ A problem on Hartman and Wintner: approximation for discrete perturbations
Cites Work
- Asymptotics for orthogonal polynomials with regularly varying recurrence coefficients
- A survey of general orthogonal polynomials for weights on finite and infinite intervals
- Relative asymptotics for orthogonal polynomials with unbounded recurrence coefficients
- Asymptotics for orthogonal polynomials defined by a recurrence relation
- Géza Freud, orthogonal polynomials and Christoffel functions. A case study
- Asymptotic properties of orthogonal polynomials from their recurrence formula. II
- A proof of Freud's conjecture for exponential weights
- Asymptotics for orthogonal polynomials on and off the essential spectrum
- Strong asymptotics for extremal polynomials associated with weights on \({\mathbb{R}}\)
- Strong asymptotics for orthogonal polynomials with regularly and slowly varying recurrence coefficients
- A unified theory of regularly varying sequences
- Asymptotics of discrete orthogonal polynomials and the continuum limit of the Toda lattice
- ON ASYMPTOTIC PROPERTIES OF POLYNOMIALS ORTHOGONAL ON THE REAL AXIS
- Asymptotics for Orthogonal Polynomials Associated with $\exp ( - x^4 )$
- A Note on the WKB Method for Difference Equations
- On Asymptotic Average Properties of Zeros of Orthogonal Polynomials
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