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.

翻译：本文提出了一种广义有限差分(GFD)格式，用于有效计算模拟具有密度抑制迁移特性的菌株的抛物-椭圆型系统的数值解。GFD方法是一种无网格方法，以其在求解不规则边界非线性边值问题时的简便性而著称。本文首先介绍了GFD方法的基本要素，随后推导了一种显-隐式格式。在时间步长有界条件下证明了该方法的收敛性，并给出了其计算实现算法。最后，通过若干算例对比了规则网格与不规则点云下的计算结果。