A Legendre–Galerkin Chebyshev collocation method for the Burgers equation with a random perturbation on boundary condition
A Legendre–Galerkin Chebyshev collocation method for the Burgers equation with a random perturbation on boundary condition
复制标题
边界条件随机扰动的Burgers方程的Legendre-Galerkin Chebyshev配置方法
DOI：
10.1002/mma.8620
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发表时间：
2022
影响因子：
2.9
通讯作者：
Hua Wu
中科院分区：
文献类型：
--
作者：
Jiajia Pan;Hua Wu
本文将广义多项式混沌展开和谱方法应用于Burgers型方程的左边界条件具有随机扰动的情形。首先，采用随机Galerkin方法和Legendre-Galerkin-Chebyshev配置格式相结合的方法，即用随机Galerkin方法将原始方程转化为确定性的非线性方程组，并用Legendre-Galerkin-Chebyshev配置格式处理得到的非线性方程组。其次，提出了求解随机Burgers方程的随机Legendre-Galerkin-Chebyshev配置格式，即用随机Legendre-Galerkin方法离散随机变量，同时通过Chebyshev-Gauss点内插非线性项。与已有的求解随机Burgers方程的方法不同，该方法可以得到一组确定的线性方程。分析了前一种方法的均方收敛性能。数值实验表明了这两种方法的有效性。这两种方法都为处理具有非线性项的随机微分方程解提供了另一种途径。
In the paper, we apply the generalized polynomial chaos expansion and spectral methods to the Burgers equation with a random perturbation on its left boundary condition. Firstly, the stochastic Galerkin method combined with the Legendre–Galerkin Chebyshev collocation scheme is adopted, which means that the original equation is transformed to the deterministic nonlinear equations by the stochastic Galerkin method and the Legendre–Galerkin Chebyshev collocation scheme is used to deal with the resulting nonlinear equations. Secondly, the stochastic Legendre–Galerkin Chebyshev collocation scheme is developed for solving the stochastic Burgers equation; that is, the stochastic Legendre–Galerkin method is used to discrete the random variable meanwhile the nonlinear term is interpolated through the Chebyshev–Gauss points. Then a set of deterministic linear equations can be obtained, which is in contrast to the other existing methods for the stochastic Burgers equation. The mean square convergence of the former method is analyzed. Numerical experiments are performed to show the effectiveness of our two methods. Both methods provide alternative approaches to deal with the stochastic differential equations with nonlinear terms.
DOI：
10.1146/annurev.fl.19.010187.002011
发表时间：
1987
期刊：
--
影响因子：
--
作者：
C. Canuto;M. Hussaini;A. Quarteroni;T. Zang
通讯作者：
C. Canuto;M. Hussaini;A. Quarteroni;T. Zang