Accurate spectral collocation computations of high order eigenvalues for singular Schrödinger equations-revisited

Abstract

In this paper, we continue to solve as accurately as possible singular eigenvalues problems attached to the Schrödinger equation. We use the conventional ChC and SiC as well as Chebfun. In order to quantify the accuracy of our outcomes, we use the drift with respect to some parameters, i.e., the order of approximation N, the length of integration interval X, or a small parameter ε, of a set of eigenvalues of interest. The deficiency of orthogonality of eigenvectors, which approximate eigenfunctions, is also an indication of the accuracy of the computations. The drift of eigenvalues provides an error estimation and, from that, one can achieve an error control. In both situations, conventional spectral collocation or Chebfun, the computing codes are simple and very efficient. An example for each such code is displayed so that it can be used. An extension to a 2D problem is also considered.

Authors

Calin-Ioan Gheorghiu
Tiberiu Popoviciu Institute of Numerical Analysis, Romanian Academy

Keywords

Schrödinger eigenproblem; singularities; Chebyshev collocation; Chebfun; error estimation; Weierstrass spectrum; eigenvalue level crossing

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Cite this paper as:

C.I. Gheorghiu, Accurate spectral collocation computations of high order eigenvalues for singular Schrödinger equations-revisited, Symmetry, 13 (2021) 5, https://doi.org/10.3390/sym13050761

About this paper

Journal

Symmetry

Publisher Name

MDPI

Print ISSN

2227-7390

Online ISSN

Not available yet.

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