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首页> 外文期刊>Applied mathematics letters >Numerical solutions of Burgers' equation with random initial conditions using the Wiener chaos expansion and the Lax-Wendroff scheme
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Numerical solutions of Burgers' equation with random initial conditions using the Wiener chaos expansion and the Lax-Wendroff scheme

机译：使用维纳混沌展开和Lax-Wendroff方案的具有初始初始条件的Burgers方程的数值解

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摘要

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. (C) 2006 Elsevier Ltd. All rights reserved.
机译：这项工作涉及具有初始初始条件的Burgers方程解的统计矩的有效计算。当使用维纳混沌扩展（WCE）扩展Lax-Wendroff方案时，它引入了一个关于非随机Hermite-Fourier系数的确定性方程式的无限系统。系统的重要特性之一是可以使用仅涉及系统解的简单公式来计算解的所有统计矩。 WCE计算统计矩的方法的稳定性，准确性和效率已经过数值测试，并与蒙特卡洛（MC）方法进行了比较。强有力的证据表明，至少对于某些类型的初始条件，WCE方法与MC方法一样准确，但比MC方法更快。 （C）2006 Elsevier Ltd.保留所有权利。

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