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Mathematical Problems in Engineering
Volume 2006, Article ID 17406, 21 pages
http://dx.doi.org/10.1155/MPE/2006/17406

An efficient computational method for statistical moments of Burger's equation with random initial conditions

Department of Mathematics, Korea University, 1 Anamdong, Sungbuk-ku, Seoul 136-701, South Korea

Received 15 November 2005; Revised 4 July 2006; Accepted 12 September 2006

Copyright © 2006 Hongjoong Kim. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The paper is concerned with efficient computation of numerical solutions to Burger's equation with random initial conditions. When the Lax-Wendroff scheme (LW) is expanded using the Wiener chaos expansion (WCE), random and deterministic effects can be separated and we obtain a system of deterministic equations with respect to Hermite-Fourier coefficients. One important property of the system is that all the statistical moments of the solution to the Burger's equation can be computed using the solution of the system only. Thus LW with WCE presents an alternative to computing moments by the Monte Carlo method (MC). It has been numerically demonstrated that LW with WCE approach is equally accurate but substantially faster than MC at least for certain classes of initial conditions.