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This decomposition is worth writing out because it names what a reported simulation number actually is: not the true answer f(x) , but a sum of the true answer with a discretization error that shrinks with step size h , a rounding error governed by machine precision u , and — the term simulations share with no other approach on this list — an irreducible modeling error from every simplifying assumption baked into the equations themselves before any computer touches them. A formal proof and a peer-reviewed argument both aim at f(x) exactly; a simulation reports $\hat{f}(x)$ and, if it is honest, reports an estimate of how large the three error terms might be.

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