A Neumann series of Bessel functions representation for solutions of perturbed Bessel equations

DOI10.1080/00036811.2017.1284313zbMath1395.34016arXiv1609.06679OpenAlexW3098316685MaRDI QIDQ4576763

Vladislav V. Kravchenko, Raúl Castillo-Pérez, Sergii M. Torba

Publication date: 10 July 2018

Published in: Applicable Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1609.06679

zbMATH Keywords

numerical methodsspectral problemsLegendre polynomialsNeumann series of Bessel functionstransmutation operatorrepresentation of solutionperturbed Bessel equationconvergent rate estimates

Mathematics Subject Classification ID

Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) (34L40) Sturm-Liouville theory (34B24) Asymptotic approximations, asymptotic expansions (steepest descent, etc.) (41A60) Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.) (42C10) Analytical theory of ordinary differential equations: series, transformations, transforms, operational calculus, etc. (34A25) Approximation by polynomials (41A10) Rate of convergence, degree of approximation (41A25) Special ordinary differential equations (Mathieu, Hill, Bessel, etc.) (34B30)

Related Items (14)

Energy decay for a degeneratewave equation under fractional derivative controls ⋮ Theory of generalized Bessel potential space and functional completion ⋮ Spectrum completion and inverse Sturm–Liouville problems ⋮ Supersymmetric generalized power functions ⋮ Some Recent Developments in the Transmutation Operator Approach ⋮ Inversion of Hyperbolic B-Potentials ⋮ On a series representation for integral kernels of transmutation operators for perturbed Bessel equations ⋮ A Neumann series of Bessel functions representation for solutions of Sturm-Liouville equations ⋮ Construction of a transmutation for the one-dimensional Schrödinger operator and a representation for solutions ⋮ Applications of integral transforms composition method (ITCM) to wave-type singular differential equations and index shift transmutations ⋮ A representation of the transmutation kernels for the Schrödinger operator in terms of eigenfunctions and applications ⋮ Integral representation for Bessel's functions of the first kind and Neumann series ⋮ Analytic approximation of transmutation operators for one-dimensional stationary Dirac operators and applications to solution of initial value and spectral problems ⋮ Inverse spectral problems for radial Schrödinger operators and closed systems

Uses Software

• MATSLISE

Cites Work

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• Analytic approximation of transmutation operators and applications to highly accurate solution of spectral problems
• On the singular Weyl-Titchmarsh function of perturbed spherical Schrödinger operators
• Spectral parameter power series for perturbed Bessel equations
• Spectral theory of ordinary differential operators
• Inverse spectral theory for a singular Sturm-Liouville operator on \([0,1\)]
• Expansion in series of Bessel functions and transmutations for perturbed Bessel operators
• Representation of solutions to the one-dimensional Schrödinger equation in terms of Neumann series of Bessel functions
• Inverse eigenvalue problems for perturbed spherical Schrödinger operators
• Neumann series of Bessel functions
• Eigenvalue problems, spectral parameter power series, and modern applications
• Spectral parameter power series method for discontinuous coefficients
• Computing eigenvalues of Sturm-Liouville systems of Bessel type
• A Uniform Expansion for the Eigenfunction of a Singular Second-Order Differential Operator
• Transmutations and Spectral Parameter Power Series in Eigenvalue Problems
• Spectral parameter power series for Sturm–Liouville problems
• Generalized wave polynomials and transmutations related to perturbed Bessel equations
• Matslise 2.0
• Neumann Series of Bessel Functions

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