Discrete Dynamics in Nature and Society
Volume 2009 (2009), Article ID 584718, 15 pages
doi:10.1155/2009/584718
Modified Crank-Nicolson difference schemes for nonlocal boundary value problem for the Schrödinger equation
Allaberen Ashyralyev1
and Ali Sirma2
1Department of Mathematics, Fatih University, 34500 Büyükcekmece, Istanbul, Turkey
2Department of Mathematics and Computer Sciences, Bahcesehir University, Besiktas, 34353 Istanbul, Turkey
Abstract
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.