Related papers: Generalized spheroidal wave equation for real and …
In this article we are interested for the numerical study of nonlinear eigenvalue problems. We begin with a review of theoretical results obtained by functional analysis methods, especially for the Schrodinger pencils. Some recall are given…
The general method to obtain solutions of the Maxwellian equations from scalar representatives is developed and applied to the diffraction of electromagnetic waves. Kirchhoff's integral is modified to provide explicit expressions for these…
Single-particle resonance parameters and wave functions in spherical and deformed nuclei are determined through analytic continuation in the potential strength. In this method, the analyticity of the eigenvalues and eigenfunctions of the…
As demonstrated by Slepian et. al. in a sequence of classical papers, prolate spheroidal wave functions (PSWFs) provide a natural and efficient tool for computing with bandlimited functions defined on an interval. As a result, PSWFs are…
In solid-state physics, energies of crystals are usually computed with a plane-wave discretization of Kohn-Sham equations. However the presence of Coulomb singularities requires the use of large plane-wave cut-offs to produce accurate…
We propose an adaptive planewave method for eigenvalue problems in electronic structure calculations. The method combines a priori convergence rates and accurate a posteriori error estimates into an effective way of updating the energy…
We give formulae for first and second derivatives of generalized eigenvalues/eigenvectors of symmetric matrices and generalized singular values/singular vectors of rectangular matrices when the matrices are linear or nonlinear functions of…
The generalized second-order partial derivatives of 1/r, where r is the radial distance in 3D, are obtained using a result of the potential theory of classical analysis. Some non-spherical regularization alternatives to the standard…
Fundamental rules and definitions of Fractional Differintegrals are outlined. Factorizing 1-D and 2-D Helmholtz equations four fractional eigenfunctions are determined. The functions exhibit incident and reflected plane waves as well as…
A computational linear stability analysis of spiral waves in a reaction-diffusion equation is performed on large disks. As the disk radius R increases, eigenvalue spectra converge to the absolute spectrum predicted by Sandstede and Scheel.…
We study the wave equation on one-dimensional self-similar fractal structures that can be analyzed by the spectral decimation method. We develop efficient numerical approximation techniques and also provide uniform estimates obtained by…
Generalized Prolate Spheroidal Functions (GPSF) are the eigenfunctions of the truncated Fourier transform, restricted to D-dimensional balls in the spatial domain and frequency domain. Despite their useful properties in many applications,…
The main result of this thesis is an efficient protocol to determine the frequencies of a signal $C(t)= \sum_k |a_k|^2 e^{i \omega_k t}$, which is given for a finite time, to a high degree of precision. Specifically, we develop a theorem…
In this paper, we introduce the prolate spheroidal wave functions (PSWFs) of real order $\alpha>-1$ on the unit ball in arbitrary dimension, termed as ball PSWFs. They are eigenfunctions of both a weighted concentration integral operator,…
Non-Hermitian generalized eigenvalue problems (GEPs) play a significant role in many practical applications, such as mechanical engineering. Based on the generalized Schur decomposition, we propose a variational quantum algorithm for…
This paper is concerned with the study, by computational means, of the generation and stability of solitary-wave solutions of generalized versions of the Benjamin equation. The numerical generation of the solitary-wave profiles is…
The perturbation method in supersymmetric quantum mechanics (SUSYQM) is used to study the spheroidal wave functions' recurrence relations, which are revealed by the shape-invariance property of the super-potential. The super-potential is…
We present a dissipative algorithm for solving nonlinear wave-like equations when the initial data is specified on characteristic surfaces. The dissipative properties built in this algorithm make it particularly useful when studying the…
The generalized regularized long wave (GRLW) equation has been developed to model a variety of physical phenomena such as ion-acoustic and magnetohydrodynamic waves in plasma, nonlinear transverse waves in shallow water and phonon packets…
Exact solution of Schrodinger equation for the pseudoharmonic potential is obtained for an arbitrary angular momentum. The energy eigenvalues and corresponding eigenfunctions are calculated by Nikiforov-Uvarov method. Wavefunctions are…