Modified Crank-Nicolson Difference Schemes for Nonlocal Boundary Value Problem for the Schrödinger Equation

The nonlocal boundary value problem for Schrödinger equation in a Hilbert space is considered. The 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 e...

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Bibliographic Details
Main Authors: Allaberen Ashyralyev, Ali Sirma
Format: Article
Language:English
Published: Wiley 2009-01-01
Series:Discrete Dynamics in Nature and Society
Online Access:http://dx.doi.org/10.1155/2009/584718
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Summary:The nonlocal boundary value problem for Schrödinger equation in a Hilbert space is considered. The 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 procedure of modified Gauss elimination method is used for solving these difference schemes. The method is illustrated by numerical examples.
ISSN:1026-0226
1607-887X