A physical system of interest is described, usually in some kind of modeling program The system’s initial state is described, usually also in the same program The system description and initial state are compiled into a form understood by the simulation program The simulation program is executed, usually to derive the state of the system (within a margin of error) after some period of time has passed The simulation program’s output state is translated back to the modeling program, or some other such human-usable form $$ \begin{bmatrix}1 & 0 \\ 0 & 1\end{bmatrix}U(t) = \begin{bmatrix}1 & 0 \\ 0 & 1\end{bmatrix} \left( \cos(t) - i \begin{bmatrix} 1 & 0 \\ 0 & -1 \end{bmatrix}\sin(t) \right) $$ $$ U(t) = \begin{bmatrix}\cos(t) & 0 \\ 0 & \cos(t)\end{bmatrix} - \begin{bmatrix} i\sin(t) & 0 \\…