New variable-step algorithms for computing eigenvalues of the one-dimensional Schrödinger equation
type: Item
instance of: scholarly article
title: New variable-step algorithms for computing eigenvalues of the one-dimensional Schrödinger equation
zbMATH Open document ID: 0911.65069
author: G. Tougelidis
author: T. E. Simos
published in: Computational Mechanics
publication date: 1999-03-02T00:00:00Z
review text: Two variable-step algorithms have been developed for computing eigenvalues of the radial Schrödinger equation. The eigenvalues are computed directly as roots of a function known in transmission line theory as the impendance. The novel numerical algorithms are based also on the piecewise perturbation analysis. The first new variable-step method is based on two methods, one with zeroth-order solution and the other with first-order perturbative corrections. The second method called `` block method'' is based on three methods, one with zeroth-order solution, another with first-order perturbative corrections and another with second-order perturbative corrections. Numerical results presented indicate the efficiency of the new variable-step methods.
Mathematics Subject Classification ID: 65L15
Mathematics Subject Classification ID: 65L12
Mathematics Subject Classification ID: 34L15
Mathematics Subject Classification ID: 34L40
zbMATH DE Number: 1221215
zbMATH Keywords: numerical examples
zbMATH Keywords: eigenvalue problems
zbMATH Keywords: perturbation analysis
zbMATH Keywords: variable-step algorithms
zbMATH Keywords: radial Schrödinger equation
zbMATH Keywords: block method
reviewed by: Karel Najzar
MaRDI profile type: Publication
full work available at URL: s004660050321
OpenAlex ID: W2076053461
DOI: 10.1007/S004660050321
description: scientific article; zbMATH DE number 1221215