NSFD discretizations of interacting population models satisfying conservation laws
We consider the roles conservation laws can play in providing restrictions on the construction of finite difference discretizations of interacting population systems, modeled by coupled ordinary differential equations. Our analysis is formulated within the nonstandard finite difference (NSFD) methodology of Mickens. A major feature of this paper is the recognition that several distinct types of conservation laws exist. Using a number of well-known population models, we illustrate the details of our procedures by constructing appropriate NSFD discretizations. The relevance of these results to various issues associated with the numerical integration of the original population system differential equations is also presented, especially the role of positivity of the solutions.
population models conservation laws nonstandard finite difference method exact schemes