A simulation can produce precise numbers while solving the wrong problem. Two complementary questions keep computational models honest.

Verification asks whether the equations have been solved correctly. It concerns implementation, discretization, algebra, and numerical error. Typical checks include comparison with an analytic solution in a special case, mesh or timestep refinement, conservation tests, and independent implementations.

Validation asks whether the equations and parameters adequately represent the physical system for the intended purpose. It compares model predictions with experimental observations while accounting for measurement uncertainty and model assumptions.

Suppose a numerical pendulum model predicts a period of $2.006,\mathrm{s}$. Refining the timestep from $10^{-2}$ to $5\times10^{-3},\mathrm{s}$ changes the prediction by only $0.001,\mathrm{s}$ and an analytic small-angle solution agrees. These are verification checks. If a real pendulum measured over many trials has period $2.08\pm0.02,\mathrm{s}$, the remaining discrepancy is not fixed by using an even smaller timestep. The model may need finite-amplitude, air-drag, pivot-friction, or geometry corrections: that is a validation issue.

A useful hierarchy is: verify code against known mathematics, quantify numerical convergence, then validate the physical model against data. Agreement with one experiment does not validate a model universally; validation is always tied to a range of conditions and observables.

Verification separates numerical error from modeling error. Validation separates mathematical consistency from empirical adequacy. Treating them as different tasks prevents computational sophistication from hiding weak physics.