Analysis of mathematical methods and principles of molecular dynamics and monte carlo method

Abstract

In this era, molecular dynamics and Monte Carlo methods have become the primary simulation methods. With the emergence of computer simulation research methods, it has been possible to solve the sizeable computational volume and some other problems in the simulation process. At present, molecular dynamics simulations have taken an essential place in the substantial computational system and have a remarkable ability to solve multi-body problems. Therefore, researchers widely use it in many fields such as physics, chemistry, and materials science. Meanwhile, the Monte Carlo method is also a very effective statistical simulation method. This method can far surpass ordinary integration in efficiency with guaranteed computational accuracy. Furthermore, the derived kinetic Monte Carlo method can simulate and study dynamics problems. It can be seen that both simulation methods play an vital role in various disciplines. Therefore, it is very significant to understand the mathematical principles behind them and to know their advantages and disadvantages.