A multirate numerical scheme for large-scale vehicle traffic simulation
  Nowadays the city-wide traffic contains hundreds of thousands of vehicles with different scenarios of their behavior. If a microscopic approach is used it leads to solving tremendous systems of ordinary differential equations whose components have a wide range of variation rates. The given paper has introduced a multirate numerical scheme with a self-adjusting time stepping strategy. Instead of using a single step size for the whole system we have determined the step size for each component by estimating its own local variation. We also performed the stability analysis for the developed scheme. The presented multirate scheme provides a significant speed-up in processor times compared to the corresponding single-rate one. The use of multiple time steps admits parallel computing. 
Valentina Kurtc, Igor Anufriev
physics.soc-ph