Modified Crank-Nicolson Difference Schemes for Nonlocal Boundary Value Problem for the Schrödinger Equation - Allaberen Ashyralyev; Ali Sirma (Discrete Dynamics in Nature and Society)
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.