Finite-difference methods for simulation models incorporating   non-conservative forces
  We discuss algorithms applicable to the numerical solution of second-order ordinary differential equations by finite-differences. We make particular reference to the solution of the dissipative particle dynamics fluid model, and present extensive results comparing one of the algorithms discussed with the standard method of solution. These results show the successful modeling of phase separation and surface tension in a binary immiscible fluid mixture. 
Keir E. Novik and Peter V. Coveney