| Autor: |
Lin Zhang, Yongbin Ge, Zhi Wang |
| Jazyk: |
angličtina |
| Rok vydání: |
2022 |
| Předmět: |
|
| Zdroj: |
Mathematical Biosciences and Engineering, Vol 19, Iss 7, Pp 6764-6794 (2022) |
| Druh dokumentu: |
article |
| ISSN: |
1551-0018 |
| DOI: |
10.3934/mbe.2022319?viewType=HTML |
| Popis: |
The paper is concerned with development of an accurate and effective positivity-preserving high-order compact difference method for solving the Keller-Segel chemotaxis model, which is a kind of nonlinear parabolic-parabolic system in mathematical biology. Firstly, a stiffly-stable five-step fourth-order fully implicit compact difference scheme is proposed. The new scheme not only has fourth-order accuracy in the spatial direction, but also has fourth-order accuracy in the temporal direction, and the computational strategy for the nonlinear chemotaxis term is provided. Then, a positivity-preserving numerical algorithm is presented, which ensures the non-negativity of cell density at all time without accuracy loss. And a time advancement algorithm is established. Finally, the proposed method is applied to the numerical simulation for chemotaxis phenomena, and the accuracy, stability and positivity-preserving of the new scheme are validated with several numerical examples. |
| Databáze: |
Directory of Open Access Journals |
| Externí odkaz: |
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