The effect of splitting strategy on qualitative property preservation

It is common for mathematical models of physical systems to possess qualitative properties such as positivity, monotonicity, or conservation of underlying physical behavior. When these models consist of differential equations, it is also common for them to be solved via splitting, i.e., splitting the differential equations into parts that are integrated separately. All splitting strategies are not created equal; however, in this work, we study the effect of two splitting strategies on qualitative property preservation applied to the basic susceptible-infected-recovered (SIR) model from epidemiology and the effect of backward integration of operator-splitting methods on positivity preservation in the Robertson test problem. We find that qualitative property preservation does depend on the splitting strategy even if the sub-integrations are performed exactly. Accordingly, the specific choice of splitting strategy used may be informed by requirements of qualitative property preservation. The choice of operator-splitting method also depends on the specific properties of the exact solution of the sub-systems.