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

Allaberen Ashyralyev | Zendy; Ali Sırma | Zendy

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

Author(s) -

Allaberen Ashyralyev,

Ali Sırma

Publication year - 2009

Publication title -

discrete dynamics in nature and society

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.264

H-Index - 39

eISSN - 1607-887X

pISSN - 1026-0226

DOI - 10.1155/2009/584718

Subject(s) - mathematics , crank–nicolson method , boundary value problem , dirichlet boundary condition , mathematical analysis , stability (learning theory) , space (punctuation) , schrödinger equation , hilbert space , finite difference method , computer science , machine learning , operating system

The nonlocal boundary value problem for Schrödinger equation in a Hilbert spaceis considered. The second-order of accuracy -modified Crank-Nicolson difference schemes for theapproximate solutions of this nonlocal boundary value problem are presented. The stability of thesedifference schemes is established. A numerical method is proposed for solving a one-dimensionalnonlocal 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

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