论文标题
模型的正则化解决方案的最佳收敛，描述了由分数布朗纸噪声驱动的超扩散和亚散射之间的竞争
Optimal convergence for the regularized solution of the model describing the competition between super- and sub- diffusions driven by fractional Brownian sheet noise
论文作者
论文摘要
超级和下扩散是自然世界中两种典型的异常扩散类型。在这项工作中，我们讨论了描述由小部分布朗纸噪声驱动的超级扩散和下扩散之间竞争的模型的数值方案。基于解决方案获得的调节结果，通过使用Mittag-Leffler函数的特性和Wong-Zakai近似的正则噪声，我们充分利用解决方案操作员的规律性来实现正则化解决方案的最佳收敛。光谱Galerkin方法和Mittag-Leffler Euler集成符分别用于处理空间和时间操作员。特别是，通过Contour积分，实现了Mittag-Leffler Euler Integrator的快速评估。我们提供了完整的错误分析，这些分析通过数值实验验证。
Super- and sub- diffusions are two typical types of anomalous diffusions in the natural world. In this work, we discuss the numerical scheme for the model describing the competition between super- and sub- diffusions driven by fractional Brownian sheet noise. Based on the obtained regulization result of the solution by using the properties of Mittag-Leffler function and the regularized noise by Wong-Zakai approximation, we make full use of the regularity of the solution operators to achieve optimal convergence of the regularized solution. The spectral Galerkin method and the Mittag-Leffler Euler integrator are respectively used to deal with the space and time operators. In particular, by contour integral, the fast evaluation of the Mittag-Leffler Euler integrator is realized. We provide complete error analyses, which are verified by the numerical experiments.
