Fourth-order finite difference scheme and efficient algorithm for nonlinear fractional Schrödinger equations
Abstract To improve the computing efficiency, a fourth-order difference scheme is proposed and a fast algorithm is designed to simulate the nonlinear fractional Schrödinger (FNLS) equation oriented from the fractional quantum mechanics. The numerical analysis and experiments conducted in this articl...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2020-01-01
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| Series: | Advances in Difference Equations |
| Subjects: | |
| Online Access: | https://doi.org/10.1186/s13662-019-2435-3 |
| _version_ | 1819299101628432384 |
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| author | Yan Chang Huanzhen Chen |
| author_facet | Yan Chang Huanzhen Chen |
| author_sort | Yan Chang |
| collection | DOAJ |
| description | Abstract To improve the computing efficiency, a fourth-order difference scheme is proposed and a fast algorithm is designed to simulate the nonlinear fractional Schrödinger (FNLS) equation oriented from the fractional quantum mechanics. The numerical analysis and experiments conducted in this article show that the proposed difference scheme has the optimal second-order and fourth-order convergence rates in time and space respectively, reduces its computation cost to O(MlogM) $\mathcal{O}(M\log M)$, and recognizes accurately its physical feature of FNLS such as the mass balance. |
| first_indexed | 2024-12-24T05:40:27Z |
| format | Article |
| id | doaj.art-e31a3b7c3344407c8762744d61beb6d6 |
| institution | Directory Open Access Journal |
| issn | 1687-1847 |
| language | English |
| last_indexed | 2024-12-24T05:40:27Z |
| publishDate | 2020-01-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Advances in Difference Equations |
| spelling | doaj.art-e31a3b7c3344407c8762744d61beb6d62022-12-21T17:12:51ZengSpringerOpenAdvances in Difference Equations1687-18472020-01-012020111810.1186/s13662-019-2435-3Fourth-order finite difference scheme and efficient algorithm for nonlinear fractional Schrödinger equationsYan Chang0Huanzhen Chen1School of Mathematics and Statistics, Shandong Normal UniversitySchool of Mathematics and Statistics, Shandong Normal UniversityAbstract To improve the computing efficiency, a fourth-order difference scheme is proposed and a fast algorithm is designed to simulate the nonlinear fractional Schrödinger (FNLS) equation oriented from the fractional quantum mechanics. The numerical analysis and experiments conducted in this article show that the proposed difference scheme has the optimal second-order and fourth-order convergence rates in time and space respectively, reduces its computation cost to O(MlogM) $\mathcal{O}(M\log M)$, and recognizes accurately its physical feature of FNLS such as the mass balance.https://doi.org/10.1186/s13662-019-2435-3Fractional Schrödinger equationFourth-order difference schemeFast algorithmMass balanceNumerical analysis |
| spellingShingle | Yan Chang Huanzhen Chen Fourth-order finite difference scheme and efficient algorithm for nonlinear fractional Schrödinger equations Advances in Difference Equations Fractional Schrödinger equation Fourth-order difference scheme Fast algorithm Mass balance Numerical analysis |
| title | Fourth-order finite difference scheme and efficient algorithm for nonlinear fractional Schrödinger equations |
| title_full | Fourth-order finite difference scheme and efficient algorithm for nonlinear fractional Schrödinger equations |
| title_fullStr | Fourth-order finite difference scheme and efficient algorithm for nonlinear fractional Schrödinger equations |
| title_full_unstemmed | Fourth-order finite difference scheme and efficient algorithm for nonlinear fractional Schrödinger equations |
| title_short | Fourth-order finite difference scheme and efficient algorithm for nonlinear fractional Schrödinger equations |
| title_sort | fourth order finite difference scheme and efficient algorithm for nonlinear fractional schrodinger equations |
| topic | Fractional Schrödinger equation Fourth-order difference scheme Fast algorithm Mass balance Numerical analysis |
| url | https://doi.org/10.1186/s13662-019-2435-3 |
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