Abstract
Accurate numerical methods that also preserve the important properties of dynamical systems are essential, especially when approximating systems in science and engineering. In this paper, we analyze a simple growth model in the chemostat and present a new higher-order nonstandard finite difference (NSFD) method for it, which is positivity-preserving, elementary stable, and also of second-order accuracy. A set of numerical simulations is also presented to support the theoretical results.