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

Allaberen Ashyralyev and Ali Sirma

Discrete Dynamics in Nature and Society, 2009, vol. 2009, 1-15

Abstract:

The nonlocal boundary value problem for Schrödinger equation in a Hilbert space is considered. The second-order of accuracy ð ‘Ÿ -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.

Date: 2009
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnddns:584718

DOI: 10.1155/2009/584718

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