How to validate mathematical equations which govern a process/ phenomenon?
I have few mathematical models which govern a mechanical phenomenon..Experimentation is not possible..hence I want to do the validation.
From your description it appears that what is required are mathematical proofs. I suggest consulting a good physicist, engineer and/or an applied mathematician.
Best, David Booth
What process, what phenomena? Do you have parameters that need to be calibrated? How many simultaneously? Do you observational data to compare to the model. Or are you asking about internal consistency of the equations?
As long you are dealing with a physically observable process, there has to one or more observable process properties/parameters which may be functionally dependant on the process equations you have derieved, through several sucessive layers of intermediate variables and associated functions interrelating them, you need to unravel these layers by a thorough analysids of the process, i.e. start with one or more observables of the process and try to link them to your derieved equations, by using either hard computing, i.e. mechanistic tools or if possible some kind of simulation tools.
Without some kind of experiment (measurements) we are speaking about pure speculation, with no grounds. However, there may be some noticeable exceptions. For example, if the mathematical equation describes creation of energy from nothing then this equation has no physical sense and should be discarded.
The only property of a mathematical description that matters is consistency. And that's possible to check, either by proving the corresponding mathematical statements, or by checking them through computer simulations.
``Physical sense'' is just a synonym for ``familiarity''.
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