Approximations to the Stochastic Burgers Equation
Approximations to the Stochastic Burgers Equation
复制标题
DOI：
10.1007/s00332-011-9104-3
复制
发表时间：
2010-05
影响因子：
3
通讯作者：
Martin Hairer;J. Voss
中科院分区：
文献类型：
--
作者：
Martin Hairer;J. Voss
本文主要研究随机Burgers方程的各种有限差分近似。在一维情况下特别感兴趣的是驾驶噪声在空间和时间上都是白色的情况。我们证明，在这种情况下，不同的有限差分格式收敛到不同的限制过程的网格大小趋于零。给出了这种现象的理论解释，我们制定了一些更一般的类方程，支持数值证据的acetitures。
This article is devoted to the numerical study of various finite-difference approximations to the stochastic Burgers equation. Of particular interest in the one-dimensional case is the situation where the driving noise is white both in space and in time. We demonstrate that in this case, different finite-difference schemes converge to different limiting processes as the mesh size tends to zero. A theoretical explanation of this phenomenon is given and we formulate a number of conjectures for more general classes of equations, supported by numerical evidence.