# What is the difference between computation and simulation?

I would like to know some examples too, if you could use them in explaining in the words.

For the most part, "simulations" are a specific type of "computation". This agrees with the first lines from the Wikipedia articles for computation and simulation:

"A computation is any type of arithmetic or non-arithmetic calculation that is well-defined."

"A simulation is the imitation of the operation of a real-world process or system over time."

You asked for specific examples, so I'll think of specific examples in matter modeling. If I would like to simulate the dynamics of a protein when salt is added to its surrounding aqueous solution, I may enter all atoms of the protein and surrounding water molecules into a computer program, and use to simulate how the atoms will move when salt is added. Overall, this entire study can be considered a "simulation" but there could be millions of calculations done as part of the simulation process, and since a simulation is a specific type of calculation, the whole simulation can also be called an MD calculation.

I'll also go beyond the Wikipedia definition. When it says that a simulation imitates a "real-world process or system over time", I don't think needs to be "over time". You can simulate a static system too. Instead of doing an experiment on a stationary neon atom to find out it's ionization energy, you can simulate it on a computer by entering the number of electrons and protons into an program and calculating a numerical solution to the time-independent Schroedinger equation for the neutral atom and for its cation (the difference in the obtained ground state energies can be considered the ionization energy of our "simulated" atom, even though it remained static the whole time). This simulation, is again a special case of a computation, because we have just computed the solutions to the Schroedinger equation with two different Hamiltonians.

Can there be calculations in matter modeling that are not simulations? Yes absolutely! We do calculations all the time (matrix multiplications, root-finding, etc.) that don't need to have any interpretation as a simulation. If we're multiplying a number by $$\hbar$$ as a step in a unit conversion, that multiplication is a computation, but are you simulating anything? We can probably find a way to argue that we are, but for the most part it wouldn't be very valuable or important or necessary to think of this as a simulation.

Finally, simulations don't have to be computations, which is why my first sentence in this answer starts with "for the most part". This is sometimes called an "analog simulation". For example, we might use LEGO to build a structure that closely resembles a certain protein, then we might throw a tennis ball at the structure to see what happens when the protein is bombarded by an extremely high-energy particle. This might not be the most accurate simulation, but it's still a simulation, and it would again not be very valuable or important or necessary to call this a "computation", even if it's possible to argue that it is one.