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  • $\begingroup$ Have you tried [Mma's RandomVariate[...]](reference.wolfram.com/mathematica/ref/RandomVariate.html)? What does values do? Is there a reason you are using ExplicitEuler? You would benefit by letting Mathematica choose the solver automatically or use perhaps the magic-wand Method->"LSODA". Also, why not just let t range from 0 to a very large number (for long term behavior)? $\endgroup$ Commented Apr 24, 2014 at 13:46
  • $\begingroup$ Hi, the 'values' variable is used to store parameters k1 and k2. I do not trust the automatic solvers of Mathematica because 'R[t]' is not a continuos function. For me $t \sim 1$ is a long time behaviour. The problem presented here has a damping of momentum (second term) that happens on the timescale of $10^{-9}$. The momentum has to relax from thermal kicks obtained from 'R[t]' term. For this reason I am using constant time sampling. $\endgroup$ Commented Apr 24, 2014 at 22:32
  • $\begingroup$ May I ask if this molecular dynamics or some such? What is the physical phenomena that you are trying to model? $\endgroup$ Commented Apr 24, 2014 at 23:23
  • $\begingroup$ It is a simple 1D Molecular Dynamics model for free diffusion $\endgroup$ Commented Apr 24, 2014 at 23:40
  • $\begingroup$ I performed simulations on MD for my Master's degree and I am curious, if you don't mind. Are you simulating Argon? With periodic BCs? Is the eqn you are solving the convection-diffusion equation? In 2012 I had a similar question on SE and I am wondering if it would help you. Good luck! $\endgroup$ Commented Apr 25, 2014 at 11:56