An adaptive low-rank splitting approach for the extended Fisher--Kolmogorov equation
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2022
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| Acceso en línea: | |
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| _version_ | 1866929281685258240 |
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| author | Zhao, Yong-Liang Gu, Xian-Ming |
| author_facet | Zhao, Yong-Liang Gu, Xian-Ming |
| contents | The extended Fisher--Kolmogorov (EFK) equation has been used to describe some phenomena in physical, material and biology systems. In this paper, we propose a full-rank splitting scheme and a rank-adaptive splitting approach for this equation. We first use a finite difference method to approximate the space derivatives. Then, the resulting semi-discrete system is split into two stiff linear parts and a nonstiff nonlinear part. This leads to our full-rank splitting scheme. The convergence and the maximum principle of the proposed scheme are proved rigorously. Based on the frame of the full-rank splitting scheme, a rank-adaptive splitting approach for obtaining a low-rank solution of the EFK equation. Numerical examples show that our methods are robust and accurate. They can also preserve energy dissipation and the discrete maximum principle. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2210_15900 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | An adaptive low-rank splitting approach for the extended Fisher--Kolmogorov equation Zhao, Yong-Liang Gu, Xian-Ming Numerical Analysis The extended Fisher--Kolmogorov (EFK) equation has been used to describe some phenomena in physical, material and biology systems. In this paper, we propose a full-rank splitting scheme and a rank-adaptive splitting approach for this equation. We first use a finite difference method to approximate the space derivatives. Then, the resulting semi-discrete system is split into two stiff linear parts and a nonstiff nonlinear part. This leads to our full-rank splitting scheme. The convergence and the maximum principle of the proposed scheme are proved rigorously. Based on the frame of the full-rank splitting scheme, a rank-adaptive splitting approach for obtaining a low-rank solution of the EFK equation. Numerical examples show that our methods are robust and accurate. They can also preserve energy dissipation and the discrete maximum principle. |
| title | An adaptive low-rank splitting approach for the extended Fisher--Kolmogorov equation |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2210.15900 |