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Quasi-Monte Carlo simulation of coagulation–fragmentation

Author

Listed:
  • Lécot, Christian
  • L’Ecuyer, Pierre
  • El Haddad, Rami
  • Tarhini, Ali

Abstract

We extend a quasi-Monte Carlo scheme designed for coagulation to the simulation of the coagulation–fragmentation equation. A number N of particles is used to approximate the mass distribution. After time discretization, three-dimensional quasi-random points decide at every time step whether the particles are undergoing coagulation or fragmentation. We prove that the scheme converges as the time step is small and N is large. In a numerical test, we show that the computed solutions are in good agreement with the exact ones, and that the error of the algorithm is smaller than the error of a corresponding Monte Carlo scheme using the same discretization parameters.

Suggested Citation

  • Lécot, Christian & L’Ecuyer, Pierre & El Haddad, Rami & Tarhini, Ali, 2019. "Quasi-Monte Carlo simulation of coagulation–fragmentation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 161(C), pages 113-124.
    • Handle: RePEc:eee:matcom:v:161:y:2019:i:c:p:113-124
    DOI: 10.1016/j.matcom.2019.02.003
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    References listed on IDEAS

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    1. L’Ecuyer, Pierre & Munger, David & Lécot, Christian & Tuffin, Bruno, 2018. "Sorting methods and convergence rates for Array-RQMC: Some empirical comparisons," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 143(C), pages 191-201.
    2. Pierre L'Ecuyer & Christian Lécot & Bruno Tuffin, 2008. "A Randomized Quasi-Monte Carlo Simulation Method for Markov Chains," Operations Research, INFORMS, vol. 56(4), pages 958-975, August.
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