Modified Crank-Nicolson difference schemes for nonlocal boundary value problem for the Schrödinger equation (Q1040139)

Summary: A nonlocal boundary value problem for the Schrödinger equation in a Hilbert space is considered. 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 modified Gauss elimination method is used for solving these difference schemes. The method is illustrated by numerical examples.