@article{Xu2023, 
author = {Panpan Xu and Yongbin Ge and Lin Zhang},
title = {High-order finite difference approximation of the Keller-Segel model with additional self- and cross-diffusion terms and a logistic source},
year = {2023},
journal = {Networks and Heterogeneous Media},
volume = {18},
number = {4},
pages = {1471-1492},
keywords = {Keller-Segel chemotaxis model, logistic source, self-diffusion terms, cross-diffusion terms, finite difference method, high-order accuracy},
url = {https://www.sciopen.com/article/10.3934/nhm.2023065},
doi = {10.3934/nhm.2023065},
abstract = {In this paper, we consider the Keller-Segel chemotaxis model with self- and cross-diffusion terms and a logistic source. This system consists of a fully nonlinear reaction-diffusion equation with additional cross-diffusion. We establish some high-order finite difference schemes for solving one- and two-dimensional problems. The truncation error remainder correction method and fourth-order Padé compact schemes are employed to approximate the spatial and temporal derivatives, respectively. It is shown that the numerical schemes yield second-order accuracy in time and fourth-order accuracy in space. Some numerical experiments are demonstrated to verify the accuracy and reliability of the proposed schemes. Furthermore, the blow-up phenomenon and bacterial pattern formation are numerically simulated.}
}