TY - JOUR
T1 - Finite Difference Approximation with ADI Scheme for Two-Dimensional Keller-Segel Equations
AU - Lu , Yubin
AU - Chen , Chi-An
AU - Li , Xiaofan
AU - Liu , Chun
JO - Communications in Computational Physics
VL - 5
SP - 1352
EP - 1386
PY - 2024
DA - 2024/06
SN - 35
DO - http://doi.org/10.4208/cicp.OA-2023-0284
UR - https://global-sci.org/intro/article_detail/cicp/23195.html
KW - Keller-Segel equations, energy dissipation, positive preserving, ADI scheme.
AB - <p style="text-align: justify;">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.</p>