### Abstract

The work is concerned with efficient computation of statistical moments of solutions to Burgers' equation with random initial conditions. When the Lax-Wendroff scheme is expanded using the Wiener chaos expansion (WCE), it introduces an infinite system of deterministic equations with respect to non-random Hermite-Fourier coefficients. One of important properties of the system is that all the statistical moments of the solution can be computed using simple formulae that involve only the solution of the system. The stability, accuracy, and efficiency of the WCE approach to computing statistical moments have been numerically tested and compared to those for the Monte Carlo (MC) method. Strong evidence has been given that the WCE approach is as accurate as but substantially faster than the MC method, at least for certain classes of initial conditions.

Original language | English |
---|---|

Pages (from-to) | 545-550 |

Number of pages | 6 |

Journal | Applied Mathematics Letters |

Volume | 20 |

Issue number | 5 |

DOIs | |

Publication status | Published - 2007 May 1 |

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### Keywords

- Burgers' equation
- Lax-Wendroff scheme
- Monte Carlo method
- Wiener chaos expansion

### ASJC Scopus subject areas

- Computational Mechanics
- Control and Systems Engineering
- Applied Mathematics
- Numerical Analysis

### Cite this

**Numerical solutions of Burgers' equation with random initial conditions using the Wiener chaos expansion and the Lax-Wendroff scheme.** / Kim, Hongjoong.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - Numerical solutions of Burgers' equation with random initial conditions using the Wiener chaos expansion and the Lax-Wendroff scheme

AU - Kim, Hongjoong

PY - 2007/5/1

Y1 - 2007/5/1

N2 - The work is concerned with efficient computation of statistical moments of solutions to Burgers' equation with random initial conditions. When the Lax-Wendroff scheme is expanded using the Wiener chaos expansion (WCE), it introduces an infinite system of deterministic equations with respect to non-random Hermite-Fourier coefficients. One of important properties of the system is that all the statistical moments of the solution can be computed using simple formulae that involve only the solution of the system. The stability, accuracy, and efficiency of the WCE approach to computing statistical moments have been numerically tested and compared to those for the Monte Carlo (MC) method. Strong evidence has been given that the WCE approach is as accurate as but substantially faster than the MC method, at least for certain classes of initial conditions.

AB - The work is concerned with efficient computation of statistical moments of solutions to Burgers' equation with random initial conditions. When the Lax-Wendroff scheme is expanded using the Wiener chaos expansion (WCE), it introduces an infinite system of deterministic equations with respect to non-random Hermite-Fourier coefficients. One of important properties of the system is that all the statistical moments of the solution can be computed using simple formulae that involve only the solution of the system. The stability, accuracy, and efficiency of the WCE approach to computing statistical moments have been numerically tested and compared to those for the Monte Carlo (MC) method. Strong evidence has been given that the WCE approach is as accurate as but substantially faster than the MC method, at least for certain classes of initial conditions.

KW - Burgers' equation

KW - Lax-Wendroff scheme

KW - Monte Carlo method

KW - Wiener chaos expansion

UR - http://www.scopus.com/inward/record.url?scp=33845416495&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33845416495&partnerID=8YFLogxK

U2 - 10.1016/j.aml.2006.07.001

DO - 10.1016/j.aml.2006.07.001

M3 - Article

VL - 20

SP - 545

EP - 550

JO - Applied Mathematics Letters

JF - Applied Mathematics Letters

SN - 0893-9659

IS - 5

ER -