An explicit-implicit Generalized Finite Difference scheme for a parabolic-elliptic density-suppressed motility system
Numerical Analysis
2024-01-29 v1 Numerical Analysis
Analysis of PDEs
Abstract
In this work, a Generalized Finite Difference (GFD) scheme is presented for effectively computing the numerical solution of a parabolic-elliptic system modelling a bacterial strain with density-suppressed motility. The GFD method is a meshless method known for its simplicity for solving non-linear boundary value problems over irregular geometries. The paper first introduces the basic elements of the GFD method, and then an explicit-implicit scheme is derived. The convergence of the method is proven under a bound for the time step, and an algorithm is provided for its computational implementation. Finally, some examples are considered comparing the results obtained with a regular mesh and an irregular cloud of points.
Cite
@article{arxiv.2401.14693,
title = {An explicit-implicit Generalized Finite Difference scheme for a parabolic-elliptic density-suppressed motility system},
author = {Federico Herrero-Hervás},
journal= {arXiv preprint arXiv:2401.14693},
year = {2024}
}