### 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.

Original language | English |
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Article number | 17406 |

Journal | Mathematical Problems in Engineering |

Volume | 2006 |

DOIs | |

Publication status | Published - 2006 Dec 1 |

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### ASJC Scopus subject areas

- Engineering(all)

### Cite this

**An efficient computational method for statistical moments of Burger's equation with random initial conditions.** / Kim, Hongjoong.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - An efficient computational method for statistical moments of Burger's equation with random initial conditions

AU - Kim, Hongjoong

PY - 2006/12/1

Y1 - 2006/12/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=33845934264&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33845934264&partnerID=8YFLogxK

U2 - 10.1155/MPE/2006/17406

DO - 10.1155/MPE/2006/17406

M3 - Article

VL - 2006

JO - Mathematical Problems in Engineering

JF - Mathematical Problems in Engineering

SN - 1024-123X

M1 - 17406

ER -