Year: 2024
Author: Yubin Lu, Chi-An Chen, Xiaofan Li, Chun Liu
Communications in Computational Physics, Vol. 35 (2024), Iss. 5 : pp. 1352–1386
Abstract
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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/cicp.OA-2023-0284
Communications in Computational Physics, Vol. 35 (2024), Iss. 5 : pp. 1352–1386
Published online: 2024-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 35
Keywords: Keller-Segel equations energy dissipation positive preserving ADI scheme.