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

摘要

The nonlocal boundary value problem for Schrödinger equation in a Hilbert spaceis considered. The second-order of accuracyr-modified Crank-Nicolson difference schemes for theapproximate solutions of this nonlocal boundary value problem are presented. The stability of thesedifference schemes is established. A numerical method is proposed for solving a one-dimensionalnonlocal 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.