A hybrid stochastic method with adaptive time step control for reaction–diffusion systems

Wing-Cheong Lo City University of Hong Kong Shaokun Mao City University of Hong Kong

Data Analysis, Bio-Statistics, Bio-Mathematics mathscidoc:2104.25001

Journal of Computational Physics, 379, 392–402, 2019
Randomness often plays an important role in the spatial and temporal dynamics of biological systems. General stochastic simulation methods may lead to excessive computational cost for a system in which a large number of molecules involved. Therefore, multi-scale hybrid simulation methods become important for stochastic simulations. Here we build a spatially hybrid method which couples two approaches: discrete stochastic simulation and continuous stochastic differential equations. In our method, the locations of the interfaces between the two approaches are changing according to the distribution of molecules in a one-dimensional domain. To balance the accuracy and efficiency, the time step of the numerical method for the continuous stochastic differential equations is adapted to the dynamics of the molecules near the adaptive interfaces. The simulation results for a linear system and two nonlinear biological systems in different one-dimensional domains demonstrate the effectiveness and advantage of our new hybrid method with the adaptive time step control.
Reaction–diffusion systems, Stochastic simulation, Hybrid method, Biological patterning
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@inproceedings{wing-cheong2019a,
  title={A hybrid stochastic method with adaptive time step control for reaction–diffusion systems},
  author={Wing-Cheong Lo, and Shaokun Mao},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20210404142706238599774},
  booktitle={Journal of Computational Physics},
  volume={379},
  pages={392–402},
  year={2019},
}
Wing-Cheong Lo, and Shaokun Mao. A hybrid stochastic method with adaptive time step control for reaction–diffusion systems. 2019. Vol. 379. In Journal of Computational Physics. pp.392–402. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20210404142706238599774.
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