Universal approaches to approximate biological systems with nonstandard finite difference methods

Nonstandard finite difference methods have been extensively used to numerically solve various problems in science and engineering. Most of those methods have been specifically designed to handle each problem separately and have been difficult to extend to other problems. In recent years, general nonstandard modeling approaches preserving key characteristics of autonomous dynamical systems have been proposed. In this paper, three of these numerical methods are presented and their performance is evaluated and compared in several different settings.