Implicit finite-difference schemes, based on the Rosenbrock method, for nonlinear Schrödinger equation with artificial boundary conditions.
We investigate the effectiveness of using the Rosenbrock method for numerical solution of 1D nonlinear Schrödinger equation (or the set of equations) with artificial boundary conditions (ABCs). We compare the computer simulation results obtained during long time interval at using the finite-differen...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Public Library of Science (PLoS)
2018-01-01
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| Series: | PLoS ONE |
| Online Access: | http://europepmc.org/articles/PMC6209290?pdf=render |
| _version_ | 1818482144118308864 |
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| author | Vyacheslav A Trofimov Evgeny M Trykin |
| author_facet | Vyacheslav A Trofimov Evgeny M Trykin |
| author_sort | Vyacheslav A Trofimov |
| collection | DOAJ |
| description | We investigate the effectiveness of using the Rosenbrock method for numerical solution of 1D nonlinear Schrödinger equation (or the set of equations) with artificial boundary conditions (ABCs). We compare the computer simulation results obtained during long time interval at using the finite-difference scheme based on the Rosenbrock method and at using the conservative finite-difference scheme. We show, that the finite-difference scheme based on the Rosenbrock method is conditionally conservative one. To combine the advantages of both numerical methods, we propose new implicit and conditionally conservative combined method based on using both the conservative finite-difference scheme and conditionally conservative Rosenbrock method and investigate its effectiveness. The combined method allows decreasing the computer simulation time in comparison with the corresponding computer simulation time at using the Rosenbrock method. In practice, the combined method is effective at computation during short time interval, which does not require an asymptotic stability property for the finite-difference scheme. We generalize also the combined method with ABCs for 2D case. |
| first_indexed | 2024-12-10T11:44:18Z |
| format | Article |
| id | doaj.art-32f7b60c522d4214a8dc0b2b41553ee8 |
| institution | Directory Open Access Journal |
| issn | 1932-6203 |
| language | English |
| last_indexed | 2024-12-10T11:44:18Z |
| publishDate | 2018-01-01 |
| publisher | Public Library of Science (PLoS) |
| record_format | Article |
| series | PLoS ONE |
| spelling | doaj.art-32f7b60c522d4214a8dc0b2b41553ee82022-12-22T01:50:08ZengPublic Library of Science (PLoS)PLoS ONE1932-62032018-01-011310e020623510.1371/journal.pone.0206235Implicit finite-difference schemes, based on the Rosenbrock method, for nonlinear Schrödinger equation with artificial boundary conditions.Vyacheslav A TrofimovEvgeny M TrykinWe investigate the effectiveness of using the Rosenbrock method for numerical solution of 1D nonlinear Schrödinger equation (or the set of equations) with artificial boundary conditions (ABCs). We compare the computer simulation results obtained during long time interval at using the finite-difference scheme based on the Rosenbrock method and at using the conservative finite-difference scheme. We show, that the finite-difference scheme based on the Rosenbrock method is conditionally conservative one. To combine the advantages of both numerical methods, we propose new implicit and conditionally conservative combined method based on using both the conservative finite-difference scheme and conditionally conservative Rosenbrock method and investigate its effectiveness. The combined method allows decreasing the computer simulation time in comparison with the corresponding computer simulation time at using the Rosenbrock method. In practice, the combined method is effective at computation during short time interval, which does not require an asymptotic stability property for the finite-difference scheme. We generalize also the combined method with ABCs for 2D case.http://europepmc.org/articles/PMC6209290?pdf=render |
| spellingShingle | Vyacheslav A Trofimov Evgeny M Trykin Implicit finite-difference schemes, based on the Rosenbrock method, for nonlinear Schrödinger equation with artificial boundary conditions. PLoS ONE |
| title | Implicit finite-difference schemes, based on the Rosenbrock method, for nonlinear Schrödinger equation with artificial boundary conditions. |
| title_full | Implicit finite-difference schemes, based on the Rosenbrock method, for nonlinear Schrödinger equation with artificial boundary conditions. |
| title_fullStr | Implicit finite-difference schemes, based on the Rosenbrock method, for nonlinear Schrödinger equation with artificial boundary conditions. |
| title_full_unstemmed | Implicit finite-difference schemes, based on the Rosenbrock method, for nonlinear Schrödinger equation with artificial boundary conditions. |
| title_short | Implicit finite-difference schemes, based on the Rosenbrock method, for nonlinear Schrödinger equation with artificial boundary conditions. |
| title_sort | implicit finite difference schemes based on the rosenbrock method for nonlinear schrodinger equation with artificial boundary conditions |
| url | http://europepmc.org/articles/PMC6209290?pdf=render |
| work_keys_str_mv | AT vyacheslavatrofimov implicitfinitedifferenceschemesbasedontherosenbrockmethodfornonlinearschrodingerequationwithartificialboundaryconditions AT evgenymtrykin implicitfinitedifferenceschemesbasedontherosenbrockmethodfornonlinearschrodingerequationwithartificialboundaryconditions |