论文标题
布朗运动的数值方法，由逆向稳定稳定的下属下属的布朗运动方程
Numerical method for the Fokker-Planck equation of Brownian motion subordinated by inverse tempered stable subordinator with drift
论文作者
论文摘要
在这项工作中，基于完整的伯恩斯坦函数，我们提出了一般的规律性分析，包括最大$ \ mathrm {l}^p $规律性的fokker-planck方程，该方程控制了下属的布朗尼运动，并具有反向调节的稳定稳定的从属稳定的从属超稳定器，具有漂移的漂移。我们得出了一个广义时间 - 基于向后的Euler卷积正交的构成有限元方案，并使用经过验证的解决方案的规律性建立了数值解的最佳订单收敛。此外，该分析被推广到更通用的扩散方程。提供数值实验以支持理论结果。
In this work, based on the complete Bernstein function, we propose a generalized regularity analysis including maximal $\mathrm{L}^p$ regularity for the Fokker--Planck equation, which governs the subordinated Brownian motion with the inverse tempered stable subordinator that has a drift. We derive a generalized time--stepping finite element scheme based on the backward Euler convolution quadrature, and the optimal-order convergence of the numerical solutions is established using the proven solution regularity. Further, the analysis is generalized to more general diffusion equations. Numerical experiments are provided to support the theoretical results.
