In this paper, we discuss iterative and noniterative splitting methods, in theory and application, to solve stochastic Burgers’ equations in an inviscid form. We present the noniterative splitting methods, which are given as Lie–Trotter and Strang-splitting methods, and we then extend them to deterministic–stochastic splitting approaches. We also discuss the iterative splitting methods, which are based on Picard’s iterative schemes in deterministic–stochastic versions. The numerical approaches are discussed with respect to decomping deterministic and stochastic behaviours, and we describe the underlying numerical analysis. We present numerical experiments based on the nonlinearity of Burgers’ equation, and we show the benefits of the iterative splitting approaches as efficient and accurate solver methods.

中文翻译：

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随机Burgers方程的迭代和非迭代拆分方法：理论与应用

在本文中，我们在理论和应用上讨论了迭代和非迭代拆分方法，以无形的形式求解随机Burgers方程。我们介绍了非迭代拆分方法，分别称为Lie-Trotter和Strang-splitting方法，然后将其扩展到确定性-随机拆分方法。我们还将讨论基于确定性-随机版本的Picard迭代方案的迭代拆分方法。讨论了关于分解确定性和随机行为的数值方法，并描述了基础的数值分析。我们提供基于Burgers方程非线性的数值实验，并且我们展示了迭代拆分方法作为高效，准确的求解器方法的优势。