Results 1 to 10 of about 8,957 (53)

Analytic vs. numerical solutions to a Sturm-Liouville transmission eigenproblem

Journal of Numerical Analysis and Approximation Theory, 2019
An elliptic one-dimensional second order boundary value problem involving discontinuous coefficients, with or without transmission conditions, is considered.
Calin-Ioan Gheorghiu, Bertin Zinsou
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The parameter dependent Sturm-Liouville eigenproblem with an interior simple or double pole [PDF]

The ANZIAM Journal, 2002
AbstractBoundary value problems where resonance phenomena are studied are most often transformable to parameter dependent Sturm-Liouville (SL) eigenproblems with interior singularities. The parameter dependent Sturm-Liouville eigenproblem with interior poles is examined. Asymptotic approximations to the solutions are obtained using an extended Langer's
Acho, Thomas M., Clemence, Dominic P.
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Sturm–Liouville eigenproblems with an interior pole [PDF]

Journal of Mathematical Physics, 1981
The eigenvalues and eigenfunctions of self-adjoint Sturm–Liouville problems with a simple pole on the interior of the interval [A, B] are investigated. Three general theorems are proved and it is shown that as n→∞, the eigenfunctions more and more closely resemble those of an ordinary Sturm–Liouville problem and λn ∼−m2π2/(B−A)2, just as if there were ...
J. Boyd
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Analysis of Sturm‐Liouville Eigenproblem with Interior Singularities and a Perturbation Parameter [PDF]

Mathematical Problems in Engineering, 2014
We devote this work to the discussion underpinning the derivation of eigenvalues and eigenfunction solutions for Sturm‐Liouville boundary value problems. The study reveals that the parameter dependent nonstandard Sturm‐Liouville boundary value problem with interior singularities may have more than two turning points.
T. M. Acho
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High-order spectral collocation method using tempered fractional Sturm–Liouville eigenproblems

Computational and Applied Mathematics, 2023
AbstractThis paper presents an accurate exponential tempered fractional spectral collocation method (TFSCM) to solve one-dimensional and time-dependent tempered fractional partial differential equations (TFPDEs). We use a family of tempered fractional Sturm–Liouville eigenproblems (TFSLP) as a basis and the fractional Lagrange interpolants (FLIs) that ...
Sayed A. Dahy, Hassan ElHawary, Alaa Fahim, Tarek Aboelenen   +3 more
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A Sturm–Liouville Eigenproblem of the Fourth Kind: A Critical Latitude with Equatorial Trapping [PDF]

Studies in Applied Mathematics, 1998
Through both analytical and numerical methods, we solve the eigenproblem uzz>+(1/z−λ−(z−1/ε)2)u=0 on the unbounded interval z∈[−∞, ∞], where λ is the eigenvalue and u(z)→0 as |z|→∞. This models an equatorially trapped Rossby wave in a shear flow in the ocean or atmosphere.
Boyd, John P., Natarov, Andrei
openaire   +3 more sources

Nonrelativistic Quantum Dynamics in a Twisted Screw Spacetime

Universe
We investigate the nonrelativistic quantum dynamics of a spinless particle in a screw-type spacetime endowed with two independent twist controls that interpolate between a pure screw dislocation and a homogeneous twist.
Faizuddin Ahmed, Edilberto O. Silva
doaj   +2 more sources

Spectrum completion and inverse Sturm–Liouville problems [PDF]

Mathematical methods in the applied sciences, 2022
Given a finite set of eigenvalues of a regular Sturm–Liouville problem for the equation −y″+q(x)y=λy$$ -{y}^{{\prime\prime} }+q(x)y=\lambda y $$ , the potential q(x)$$ q(x) $$ of which is unknown.
V. Kravchenko
semanticscholar   +1 more source

Wave equation for Sturm-Liouville operator with singular potentials [PDF]

Journal of Mathematical Analysis and Applications, 2022
The paper is denoted to the initial-boundary value problem for the wave equation with the Sturm-Liouville operator with irregular (distributive) potentials.
Michael Ruzhansky, S. Shaimardan, Alibek Yeskermessuly   +2 more
semanticscholar   +1 more source

Wave Equation for Sturm–Liouville Operator with Singular Intermediate Coefficient and Potential [PDF]

Bulletin of the Malaysian Mathematical Sciences Society, 2022
In this paper, we consider a wave equation on a bounded domain with a Sturm–Liouville operator with a singular intermediate coefficient and a singular potential. To obtain and evaluate the solution, the method of separation of variables is used, then the
Michael Ruzhansky, Alibek Yeskermessuly
semanticscholar   +1 more source