Finite Difference Approximation with ADI Scheme for Two-dimensional Keller-Segel Equations

Autor:	Lu, Yubin, Chen, Chi-An, Li, Xiaofan, Liu, Chun
Rok vydání:	2023
Předmět:	Mathematics - Numerical Analysis Mathematical Physics Mathematics - Analysis of PDEs
Druh dokumentu:	Working Paper
Popis:	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. Comment: 29 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2310.20653 Zobrazit plný text záznamu View this record from Arxiv