Geodesic
Multirate numerical scheme for large-scale vehicle traffic simulation
Matematičeskoe modelirovanie, Tome 28 (2016) no. 5, pp. 124-134

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Citywide traffic contains hundreds of thousands vehicles with different scenarios of their behavior. It leads to solving tremendous ODE systems which components have wide range of variation rates in case of microscopic approach. In this paper we introduce a multirate numerical scheme with self-adjusting time stepping strategy. Instead of using a single step size for the whole system, the step size for each component is determined by estimating its own local variation. Stability analysis for developed scheme is performed and stability conditions are obtained. Presented multirate scheme provides a significant speed-up in CPU times compared to the corresponding single-rate one. The use of multiple time steps admits parallel computing.
Keywords: multirate time stepping, a priori estimates, stability, citywide microscopic traffic simulation, ordinary differential equations. 
@article{MM_2016_28_5_a8,
     author = {V. V. Kurtc and I. E. Anufriev},
     title = {Multirate numerical scheme for large-scale vehicle traffic simulation},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {124--134},
     publisher = {mathdoc},
     volume = {28},
     number = {5},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2016_28_5_a8/}
}
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V. V. Kurtc; I. E. Anufriev. Multirate numerical scheme for large-scale vehicle traffic simulation. Matematičeskoe modelirovanie, Tome 28 (2016) no. 5, pp. 124-134. http://geodesic.mathdoc.fr/item/MM_2016_28_5_a8/