Modified Crank-Nicolson Difference Schemes for Nonlocal Boundary Value Problem for the Schrödinger Equation
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 e...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2009-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2009/584718 |
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| Summary: | 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. |
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| ISSN: | 1026-0226 1607-887X |