A low-rank Lie-Trotter splitting approach for nonlinear fractional complex Ginzburg-Landau equations
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2020
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| _version_ | 1866929281588789248 |
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| author | Zhao, Yong-Liang Ostermann, Alexander Gu, Xian-Ming |
| author_facet | Zhao, Yong-Liang Ostermann, Alexander Gu, Xian-Ming |
| contents | Fractional Ginzburg-Landau equations as the generalization of the classical one have been used to describe various physical phenomena. In this paper, we propose a numerical integration method for solving space fractional Ginzburg-Landau equations based on a dynamical low-rank approximation. We first approximate the space fractional derivatives by using a fractional centered difference method. Then, the resulting matrix differential equation is split into a stiff linear part and a nonstiff (nonlinear) one. For solving these two subproblems, a dynamical low-rank approach is used. The convergence of our method is proved rigorously. Numerical examples are reported which show that the proposed method is robust and accurate. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2010_05249 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | A low-rank Lie-Trotter splitting approach for nonlinear fractional complex Ginzburg-Landau equations Zhao, Yong-Liang Ostermann, Alexander Gu, Xian-Ming Numerical Analysis Fractional Ginzburg-Landau equations as the generalization of the classical one have been used to describe various physical phenomena. In this paper, we propose a numerical integration method for solving space fractional Ginzburg-Landau equations based on a dynamical low-rank approximation. We first approximate the space fractional derivatives by using a fractional centered difference method. Then, the resulting matrix differential equation is split into a stiff linear part and a nonstiff (nonlinear) one. For solving these two subproblems, a dynamical low-rank approach is used. The convergence of our method is proved rigorously. Numerical examples are reported which show that the proposed method is robust and accurate. |
| title | A low-rank Lie-Trotter splitting approach for nonlinear fractional complex Ginzburg-Landau equations |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2010.05249 |