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A particle method for some parabolic equations

✍ Scribed by Christian Lécot; Ibrahim Coulibaly

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
846 KB
Volume
90
Category
Article
ISSN
0377-0427

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✦ Synopsis

We present a quasi-Monte-Carlo parhcle simulation of some multl&menmonal hnear parabohc equations with constant coefficients We approximate the elliptic operator m space by a fimte-dlfference operator We &scretlze time into intervals of length At The discrete representation of the solution at hme t~ = nAt is a sum of Dlrac delta measures Using the exphot Euler scheme, the resulting approxlmatlon at time t.+l is recovered by a quasi-Monte-Carlo integration We make use of a technique mvolwng renumbenng the simulated parheles m every time step We state and prove a convergence theorem for the method Experimental results are presented for some model problems The results suggest that the quasi-Monte-Carlo slmulahon tends to gwe more accurate solutmns than a Monte-Carlo simulation, when the correct renumbenng techmque is used Other choices can result m sigmficant loss of effioency @ 1998 Elsevier Science B V All nghts reserved

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