Discrete models
Simon Ya. Serovajsky · Mathematical Modelling · 2021
In practice, situations often arise when the state of the system changes discretely. In this case, the independent variables take on a finite or countable set of values. First, discusses the simplest discrete models of population dynamics. They are discrete analogues of the Malthus and Verhulst equations. Then we consider a discrete model of heat transfer in a one-dimensional body in a steady state. In contrast to these problems, the next problems are associated with the mathematical description of systems that do not have natural continuous analogues. They relate to operations research. We consider the transport problem, which consists in the rational distribution of products from points of production to points of consumption, the traveling salesman problem, which consists in choosing the optimal route for a certain number of cities,and the prisoner&s;s dilemma related to game theory. The Appendix discusses a discrete model of epidemiology and provides an additional information on the above objectives.