Modified Crank-Nicolson difference schemes for nonlocal boundary value problem for the Schrödinger equation
type: Item
instance of: scholarly article
title: Modified Crank-Nicolson difference schemes for nonlocal boundary value problem for the Schrödinger equation
zbMATH Open document ID: 1178.65096
DOI: 10.1155/2009/584718
author: Allaberen Ashyralyev
author: Ali Sirma
published in: Discrete Dynamics in Nature and Society
publication date: 2009-11-23T00:00:00Z
full work available at URL: https://eudml.org/doc/227258
review text: Summary: A nonlocal boundary value problem for the Schrödinger equation in a Hilbert space is considered. Second-order of accuracy \(r\)-modified Crank-Nicolson difference schemes for the approximate solutions of this nonlocal boundary value problem are presented. The stability of these difference schemes is established. A numerical method is proposed for solving a one-dimensional nonlocal boundary value problem for the Schrödinger equation with Dirichlet boundary condition. A modified Gauss elimination method is used for solving these difference schemes. The method is illustrated by numerical examples.
Mathematics Subject Classification ID: 65M06
Mathematics Subject Classification ID: 65M12
Mathematics Subject Classification ID: 35Q55
zbMATH DE Number: 5637370
zbMATH Keywords: nonlocal boundary value problem
zbMATH Keywords: Schrödinger equation
zbMATH Keywords: Hilbert space
zbMATH Keywords: Crank-Nicolson difference schemes
zbMATH Keywords: stability
zbMATH Keywords: Gauss elimination
zbMATH Keywords: numerical examples
Wikidata QID: Q58647502
MaRDI profile type: Publication
OpenAlex ID: W2072311810
cites work: Time-nonlocal problems for Schrödinger type equations. I: Problems in abstract spaces
cites work: Time-nonlocal problems for Schrödinger type equations. II: Results for specific problems
cites work: A finite-difference method for the one-dimensional time-dependent Schrödinger equation on unbounded domain
cites work: Growth of Sobolev norms in linear Schrödinger equations with quasi-periodic potential
cites work: Numerical schemes for the simulation of the two-dimensional Schrödinger equation using non-reflecting boundary conditions
cites work: ON WELL-POSEDNESS OF DIFFERENCE SCHEMES FOR ABSTRACT PARABOLIC EQUATIONS INLP([0,T];E) SPACES
cites work: Nonlocal boundary value problems for the Schrödinger equation
cites work: Q3516937
cites work: Well-posedness of the modified Crank-Nicolson difference schemes in Bochner spaces
cites work: Q4100565
cites work: On the modified Crankâ Nicholson difference schemes for parabolic equation with non-smooth data arising in biomechanics
description: scientific article; zbMATH DE number 5637370