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

الملخص EN

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.