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Monte Carlo and quasi-Monte Carlo algorithms for a linear integro-differential equation

  • Ibrahim Coulibaly
  • Christian Lécot
Part of the Lecture Notes in Statistics book series (LNS, volume 127)

Abstract

We consider a linear Boltzmann-type transport equation in the s-dimensional unit cube I s = [0,1) s. A quasi-Monte Carlo simulation algorithm is described. The equation is approximated by Euler’s method and the simulation makes use of a (0, 2s + 1)-sequence. In addition, we use a technique involving renumbering the simulated particles at every time step. The convergence of the quasi-Monte Carlo simulation is studied. Experimental results are presented for a model problem whose solution can be found analytically. The results show that quasi-Monte Carlo algorithms can produce more efficient solutions than standard Monte Carlo algorithms, for s < 3. Of primary importance appears to be the way to do the renumbering.

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Copyright information

© Springer Science+Business Media New York 1998

Authors and Affiliations

  • Ibrahim Coulibaly
    • 1
  • Christian Lécot
    • 1
  1. 1.Laboratoire de MathématiquesUniversité de Savoie, Campus scientifiqueLe Bourget du Lac cedexFrance

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