Copyright © 2009 Allaberen Ashyralyev and Ali Sirma. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
The nonlocal boundary value problem for Schrödinger equation in a Hilbert space
is considered. The second-order of accuracy -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.