A fully finite element approximation of the Keller–Segel model, including self-and cross-
diffusion terms and a logistic source, has been considered. The existence of a fully finite …

We study a mathematical model of cancer cell invasion of tissue (extracellular matrix)
consisting of a system of reaction–diffusion-taxis partial differential equations which …

We provide a posteriori error estimates for a discontinuous Galerkin scheme for the
parabolic-elliptic Keller-Segel system in 2 or 3 space dimensions. The estimates are …

In this paper, we prove the optimal error estimate of an unconditionally positivity-preserving,
mass-conserving and energy stable method for the Keller-Segel chemotaxis equations …

Chemotaxis systems play a crucial role in modeling the dynamics of bacterial and cellular
behaviors, including propagation, aggregation, and pattern formation, all under the influence …

We consider in this paper numerical approximation and simulation of a two-species Keller-
Segel model. The model enjoys an energy dissipation law, mass conservation and bound or …

Many microorganisms exhibit a special pattern formation at the presence of a
chemoattractant, food, light, or areas with high oxygen concentration. Collective cell …

We study a finite volume scheme approximating a parabolic-elliptic Keller–Segel system
with power-law diffusion with exponent and periodic boundary conditions. We derive …

In this paper, a type of high-order compact (HOC) finite difference method is developed for
solving two-and three-dimensional unsteady convection diffusion reaction (CDR) equations …

In this study, we introduce a new growing neural network algorithm that is based on wavelet
neural networks and call our algorithm a growing wavelet neural network (GWNN) method …