I'm not sure about the mathematical modelling bit. When I was in Uni, I was told that someone came up with a formula which mimiced the behaviour of the object. You just plugged in values and checked how the output responded. Sometimes it involved solving PDEs.
Simulation can be done in all sorts of ways. Depends on what you are simulating. The way I like to do it is by S/W integrated circuits (ICs). Basically all the components are black boxes that have inputs and outputs. You basically write a routine to handle the behaviour of the IC. The linkage of the ICs is supplied in a file. It is better to read this in in case you wish to change the linkage. You basically pass the data in, and as it goes from the output of one IC to the input of another, you call the relevant routine and change the data or behaviour accordingly. So far this technique has worked on all the simulations I've done. I must admit I used C++: not Fortran but there is nothing that says it cannot be done in Fortran.
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