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

Abstract

The nonlocal boundary value problem for Schrodinger 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 Schrodinger 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. Copyright (C) 2009