Molecular Dynamics (MD)
Methods of simulating many particle systems by solving equations of motion such as the Newton equation. Mathematically, in molecular dynamics simulation one solves a system of simultaneous ordinary differential equations by using, e.g., the Runge-Kutta method and the velocity Verlet method. While a simple implementation would allow simulation with fixed energy and fixed volume, introducing the Nose-Hoover thermostat makes it possible to simulate with fixed temperature possible as well. Similarly, simulation with fixed pressure or with chemical potential is possible. There are various choices of the force field, the interaction energy between particles, ranging from the simple short-ranged force such as the hard sphere potential and the Lennard-Jones potential to the long-ranged one such as the Coulomb potential or more realistic and more complicated ones, depending on the purpose of the simulation.