具有背景相互作用的Fokker-Planck方程的保结构随机Galerkin方法
Structure preserving stochastic Galerkin methods for Fokker-Planck equations with background interactions
摘要：
本文研究了一类具有不确定性的Fokker-Planck型方程的保结构随机Galerkin格式，该格式与外部分布（我们称之为背景分布）相互作用.所提出的方法是能够保持物理性质的统计矩的近似的问题，如非负性，熵耗散和渐近行为的预期解决方案。所介绍的方法是二阶精度的瞬态制度和高阶的大的时间。我们目前的应用程序的情况下，固定和动态背景分布的集体行为模型的发展计划。
英文摘要：
This paper is devoted to the construction of structure preserving stochastic Galerkin schemes for Fokker-Planck type equations with uncertainties and interacting with an external distribution, that we refer to as a background distribution. The proposed methods are capable to preserve physical properties in the approximation of statistical moments of the problem like nonnegativity, entropy dissipation and asymptotic behaviour of the expected solution. The introduced methods are second order accurate in the transient regimes and high order for large times. We present applications of the developed schemes to the case of fixed and dynamic background distribution for models of collective behaviour.
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