Quasilinearization method and WKB

DOI10.1016/j.cpc.2004.12.017zbMath1196.34074arXivmath-ph/0410016OpenAlexW2144348678MaRDI QIDQ709924

R. Krivec, V. B. Mandelzweig

Publication date: 18 October 2010

Published in: Computer Physics Communications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math-ph/0410016

zbMATH Keywords

nonlinear differential equationsquasilinearizationWKB

Mathematics Subject Classification ID

Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory (81Q20) Singular perturbations, turning point theory, WKB methods for ordinary differential equations (34E20) Numerical methods for ordinary differential equations (65L99)

Related Items (12)

Analytic calculation of energies and wave functions of the quartic and pure quartic oscillators ⋮ Unified QLM for regular and arbitrary singular potentials ⋮ Comparison of quasilinear and WKB approximations ⋮ Approximation of solutions for second-order \(m\)-point nonlocal boundary value problems via the method of generalized quasilinearization ⋮ An Adaptive Spectral Method for Oscillatory Second-Order Linear ODEs with Frequency-Independent Cost ⋮ Methods for solving singular perturbation problems arising in science and engineering ⋮ Initial time difference quasilinearization for Caputo fractional differential equations ⋮ Method of quasilinearization for a nonlocal singular boundary value problem in weighted spaces ⋮ Quasilinearization approach to computations with singular potentials ⋮ Approximation of solutions of the nonlinear Duffing equation involving both integral and non-integral forcing terms with separated boundary conditions ⋮ Existence and approximation of solutions of forced Duffing type integro-differential equations with three-point nonlinear boundary conditions ⋮ Accurate analytic presentation of solution for the spiked harmonic oscillator problem

Cites Work

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• A new proof for the convergent iterative solution of the degenerate quantum double-well potential and its generalization.
• Quasilinearization method and summation of the WKB series
• 1/N expansions in nonrelativistic quantum mechanics
• JWKB method and quasilinearisation
• Quasilinearisation and three-dimensional oscillators
• Quasilinearization method and its verification on exactly solvable models in quantum mechanics
• Numerical investigation of quasilinearization method in quantum mechanics
• Quasilinearization approach to nonlinear problems in physics with application to nonlinear ODEs

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