When a set of model equations, e.g. some coupled differential equations, has solutions that behave in ways similar to real-life phenomena such as blood flow in the heart, a wave movement, or a plate in free fall in some fluid (air or water), why do we call the model equations "a model for blood flow in the heart ...", etc.?

Shouldn't we call the solution/simulation "a model for blood flow in the heart ...", since it's the solution that's reproducing the phenomenon ...


If I correctly understood your question, you wonder what exactly to call "a model for blood flow in the heart": the equations or their solution.

I think part of the ambiguity comes from the fact that there are a lot of definitions of model. Even if we take only the mathematical models into considerations, there would be a lot of details and border cases to consider.

Therefore, you certainly can call the simulation/solution a model of a certain kind (say, computer model); however, that's not what is expected if we are looking at publications in computational sciences. Here, on usually considers the governing equations to constitute the [mathematical] model of the system (the square brackets indicate the usually omitted word).

Sorry for covering with the links strictly from Wikipedia. It is certainly possible to reference other sources on the modelling concepts, terminology, and even philosophy of simulations, but that's far from my area of expertise.

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