Ordinary differential equation for molecule collision
There are two types of molecular simulation (in a broad sense), namely
1) Monte Carlo simulation
2) Molecular dynamics simulation
And they can be mixed together to give rise to new algorithm. According to your problem statement I am assuming you are trying to use molecular dynamics simulation. There are lots of things you should consider for your simulation system. According to your problem statement your atoms have position and velocity, but the problem is when they will collide each other they will loose energy and will come to a halt after few time steps. Either you can use thermostat to keep the temperature constant (Anderson thermostat and Nose-Hoover thermostat), or you can use constant pressure molecular dynamics simulation. For a beginner I would like Anderson thermostat as this is very simple technique. Then you have to use Newton's second law to determine the force and velocity on each atoms. After that you can use numerical integration technique to find new position based on F=ma formulation. Now you will repeat this task to get the trajectory of individual atoms.   

If you want to find the diffusion coefficient of atoms, you can use lattice gas models or Ising models based on random Monte Carlo movement. I wrote a python code for finding diffusion coefficient. Also you can use Markov Chain Monte Carlo (MCMC) method to determice the stochastic evolution of the system.  

For your better understanding I would suggest to use Understanding Molecular Simulation by Daan Frenkel &amp; Berend Smit