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Modified Crank-Nicolson difference schemes for nonlocal boundary value problem for the Schrödinger equation. (English) Zbl 1178.65096

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.

MSC:

65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
35Q55 NLS equations (nonlinear Schrödinger equations)
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References:

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