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Electronic Journal: Southwest Journal of Pure and Applied Mathematics

Internet: http://rattler.cameron.edu/swjpam.html

ISBN 1083-0464

Issue 1 July 2004, pp. 33 – 47

Submitted: November 28, 2003. Published: July 1, 2004

AN INTERACTING PARTICLES PROCESS

FOR BURGERS EQUATION ON THE CIRCLE

ANTHONY GAMST

ABSTRACT. We adapt the results of Oelschl¨ager (1985) to prove a weak law of large numbers for an interacting particles process which, in the limit, produces a solution to Burgers equation with periodic boundary conditions. We anticipate results of this nature to be useful in the devel-opment of Monte Carlo schemes for nonlinear partial differential equa-tions.

A.M.S. (MOS) Subject Classification Codes. 35, 47, 60.

Key Words and Phrases. Burgers equation, kernel density, Kolmogorov

equation, Brownian motion, Monte Carlo scheme.

E-mail: acgamstmath.ucsd.edu

Copyright c2004 by Cameron University

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