Description
Theoretical modeling‐based analysis is a process where a model is set up based on laws of nature and logic, using mostly mathematics, physics, and engineering— initially with simplified assumptions about their processes and aiming at finding an input/output model. The following basic procedures and formulations are usually used in supporting a theoretical or an experimental model:
1. Balance equations, for stored masses, energies, and impulses
2. Physical–chemical constitutive equations
3. Phenomenological equations of irreversible processes (thermal conductivity, diffusion, chemical reaction)
4. Entropy balance equations, if several irreversible processes are interrelated
5. Connection equations, describing the interconnection of process elements
Using such formulation principles, a system can be understood in terms of their ordinary differential equations, or their algebraic equations, and then a physical device or a computer simulation or an emulation can be devised in order to obey such equations. The physical system is initialized with their proper initial values, and their development over time mimics the differential equations.
Integrators and function generation can accomplish simulation of an ordinary
differential equation (ODE). It has been discussed by Ragazzini in 1947 that the continuous functions of several variables could be approximated by a combination of scalar products, scalar functions, and their time derivatives. We have to find first suitable state variables, i.e. variables that account for energy storage. Typically those variables appear differentiated in the ordinary differential equations.