Results 1 to 10 of about 292 (68)
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
doaj +8 more sources
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.
Thomas Mbah Acho, Abdon Atangana
openaire +2 more sources
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 +3 more
openaire +2 more sources
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 +2 more sources
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.
openaire +2 more sources
A Chebyshev Spectral Method for Normal Mode and Parabolic Equation Models in Underwater Acoustics
Mathematical Problems in Engineering, Volume 2020, Issue 1, 2020., 2020 In this paper, the Chebyshev spectral method is used to solve the normal mode and parabolic equation models of underwater acoustic propagation, and the results of the Chebyshev spectral method and the traditional finite difference method are compared for an ideal fluid waveguide with a constant sound velocity and an ideal fluid waveguide with a deep ...
Houwang Tu +6 more
wiley +1 more source
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 ...
openaire +3 more sources
Vortex Structures inside Spherical Mesoscopic Superconductor Plus Magnetic Dipole
Advances in Mathematical Physics, Volume 2018, Issue 1, 2018., 2018 We investigate the existence of multivortex states in a superconducting mesoscopic sphere with a magnetic dipole placed at the center. We obtain analytic solutions for the order parameter Ψ(r→) inside the sphere through the linearized Ginzburg‐Landau (GL) model, coupled with mixed boundary conditions, and under regularity conditions and decoupling ...
A. Ludu, Alexander Iomin
wiley +1 more source
Journal of Computational and Applied Mathematics, 2004 The authors present a method for determining the eigenvalues of a Sturm-Liouville problem based on extrapolation from the discrepancy at the middle of the interval when shooting from both ends. Numerical examples are given.
GHELARDONI, PAOLO +2 more
openaire +4 more sources
Complex coordinate methods for hydrodynamic instabilities and Sturm-Liouville eigenproblems with an interior singularity [PDF]
Journal of Computational Physics, 1985 Calculations of inviscid, linearized waves in fluids are very difficult when a mean wind or current U(y) is included because the differential equation is singular wherever \(U(y)=c\), the phase speed. These ``critical latitude'', ``critical level'', or ``critical point'' singularities are particularly severe for Chebyshev methods since these global ...
openaire +2 more sources