Quasi-Monte Carlo approach to particle simulation of the heat equation

William J. Morokoff, Russel E. Caflisch

Research output: Contribution to journalArticlepeer-review


The convergence of the Monte Carlo method for numerical integration can often be improved by replacing random numbers with more uniformly distributed numbers known as quasi-random. In this paper the convergence of Monte Carlo particle simulation is studied when these quasi-random sequences are used. For the one-dimensional heat equation discretized in both space and time, convergence is proved for a quasi-random simulation using reordering of the particles according to their position. Experimental results are presented for the spatially continuous heat equation in one and two dimensions. The results indicate that a significant improvement in both magnitude of error and convergence rate can be achieved over standard Monte Carlo simulations for certain low-dimensional problems.

Original languageEnglish (US)
Pages (from-to)1558-1573
Number of pages16
JournalSIAM Journal on Numerical Analysis
Issue number6
StatePublished - 1993

ASJC Scopus subject areas

  • Numerical Analysis
  • Computational Mathematics
  • Applied Mathematics


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