Modified spectral parameter power series representations for solutions of Sturm-Liouville equations and their applications

DOI10.1016/j.amc.2014.03.153zbMath1334.34026arXiv1401.1877OpenAlexW2050138183MaRDI QIDQ275145

Sergii M. Torba, Vladislav V. Kravchenko

Publication date: 25 April 2016

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1401.1877

zbMATH Keywords

boundary value problemsinitial value problemsspectral problemsSturm-Liouville equationsnumerical methods for ODEspectral parameter expansion

Mathematics Subject Classification ID

Analytical theory of ordinary differential equations: series, transformations, transforms, operational calculus, etc. (34A25) General spectral theory of ordinary differential operators (34L05) Numerical solution of eigenvalue problems involving ordinary differential equations (65L15)

Related Items (10)

On Sturm-Liouville equations with several spectral parameters ⋮ Eigenvalue problems, spectral parameter power series, and modern applications ⋮ Analytic approximation of transmutation operators and related systems of functions ⋮ Numerical solution of vector Sturm-Liouville problems with Dirichlet conditions and nonlinear dependence on the spectral parameter ⋮ Analytic approximation of transmutation operators and applications to highly accurate solution of spectral problems ⋮ Liouville transformation, analytic approximation of transmutation operators and solution of spectral problems ⋮ Representation of solutions to the one-dimensional Schrödinger equation in terms of Neumann series of Bessel functions ⋮ The synthesis of an inhomogeneous elastic system with a boundary load ⋮ A Neumann series of Bessel functions representation for solutions of Sturm-Liouville equations ⋮ Spectral parameter power series representation for solutions of linear system of two first order differential equations

Uses Software

• MATSLISE

Cites Work

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• Analytic approximation of transmutation operators and applications to highly accurate solution of spectral problems
• Transmutations, \(L\)-bases and complete families of solutions of the stationary Schrödinger equation in the plane
• Spectral parameter power series for perturbed Bessel equations
• Semiclassical eigenvalue distribution of the Zakharov-Shabat eigenvalue problem
• Sturm-Liouville operators and applications. Transl. from the Russian by A. Iacob
• On the correction of finite difference eigenvalue approximations for Sturm-Liouville problems
• Wave polynomials, transmutations and Cauchy's problem for the Klein-Gordon equation
• A sinc-Gaussian technique for computing eigenvalues of second-order linear pencils
• Spectral parameter power series for fourth-order Sturm-Liouville problems
• Nonlinear Waves in Integrable and Nonintegrable Systems
• Solution of boundary and eigenvalue problems for second-order elliptic operators in the plane using pseudoanalytic formal powers
• Construction and application of Bergman-type reproducing kernels for boundary and eigenvalue problems in the plane
• On computing eigenvalues of second-order linear pencils
• Eigenvalue problems, spectral parameter power series, and modern applications
• Spectral parameter power series method for discontinuous coefficients
• MATSLISE
• A representation for solutions of the Sturm–Liouville equation
• Applied Pseudoanalytic Function Theory
• The Inverse Scattering Transform‐Fourier Analysis for Nonlinear Problems
• Transmutations and Spectral Parameter Power Series in Eigenvalue Problems
• Spectral parameter power series for Sturm–Liouville problems
• Dispersion equation and eigenvalues for the Zakharov-Shabat system using spectral parameter power series
• On spectra of a certain class of quadratic operator pencils with one-dimensional linear part
• Algorithm 810: The SLEIGN2 Sturm-Liouville Code

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