Finite Difference Approximation with ADI Scheme for Two-dimensional Keller-Segel Equations
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866915787142332416 |
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| author | Lu, Yubin Chen, Chi-An Li, Xiaofan Liu, Chun |
| author_facet | Lu, Yubin Chen, Chi-An Li, Xiaofan Liu, Chun |
| contents | Keller-Segel systems are a set of nonlinear partial differential equations used to model chemotaxis in biology. In this paper, we propose two alternating direction implicit (ADI) schemes to solve the 2D Keller-Segel systems directly with minimal computational cost, while preserving positivity, energy dissipation law and mass conservation. One scheme unconditionally preserves positivity, while the other does so conditionally. Both schemes achieve second-order accuracy in space, with the former being first-order accuracy in time and the latter second-order accuracy in time. Besides, the former scheme preserves the energy dissipation law asymptotically. We validate these results through numerical experiments, and also compare the efficiency of our schemes with the standard five-point scheme, demonstrating that our approaches effectively reduce computational costs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_20653 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Finite Difference Approximation with ADI Scheme for Two-dimensional Keller-Segel Equations Lu, Yubin Chen, Chi-An Li, Xiaofan Liu, Chun Numerical Analysis Mathematical Physics Analysis of PDEs Keller-Segel systems are a set of nonlinear partial differential equations used to model chemotaxis in biology. In this paper, we propose two alternating direction implicit (ADI) schemes to solve the 2D Keller-Segel systems directly with minimal computational cost, while preserving positivity, energy dissipation law and mass conservation. One scheme unconditionally preserves positivity, while the other does so conditionally. Both schemes achieve second-order accuracy in space, with the former being first-order accuracy in time and the latter second-order accuracy in time. Besides, the former scheme preserves the energy dissipation law asymptotically. We validate these results through numerical experiments, and also compare the efficiency of our schemes with the standard five-point scheme, demonstrating that our approaches effectively reduce computational costs. |
| title | Finite Difference Approximation with ADI Scheme for Two-dimensional Keller-Segel Equations |
| topic | Numerical Analysis Mathematical Physics Analysis of PDEs |
| url | https://arxiv.org/abs/2310.20653 |