A physics-informed order-of-magnitude approach to handling dynamic iterations applied to models of physical systems: Theoretical framework

In this paper, we consider (Figure presented.) -dimensional systems of differential equations applied to model a range of physical phenomena, where (Figure presented.) represents any positive integer. The defining characteristic that we focus on are the magnitudes of the inherent physical parameters, which are frequently of different orders of magnitude for various physical systems. This property, inherent to the given physical problems, can be exploited to reduce the problems into a set of much simpler subproblems, expanding our ability to gain physical insight in terms of the underlying simpler subproblems. These orders of magnitude motivate the choice of a specific class of transformations that can be chosen to reduce the number of required dynamic iterations in a sequence-based approach to examining such systems. This is also useful for the development of proof techniques for proving properties of mathematical models, such as their well-posedness.