论文标题
用LévyFlight校正BDFK的分数Feynman-kac方程
Correction of BDFk for fractional Feynman-Kac equation with Lévy flight
论文作者
论文摘要
在这项工作中，我们介绍了$ k $ step bdf卷积正交的校正公式，并以$ k-1 $ spent的$ k-1 $步骤，用于莱维飞行的分数feynman-kac方程。 通过非平滑数据可以实现所需的$ K $ th阶收敛率。基于[{\ sc jin，li和Zhou}的想法，暹罗J. Sci。 Comput。，39（2017），A3129-A3152]，我们为校正BDF $ K $方案提供了详细的收敛分析。提供了使用光谱方法的数值实验来说明提出方法的有效性。据我们所知，这是收敛分析的第一个证明，数值验证了用校正BDF $ K $验证了SAPCE分数进化方程。
In this work, we present the correction formulas of the $k$-step BDF convolution quadrature at the starting $k-1$ steps for the fractional Feynman-Kac equation with Lévy flight. The desired $k$th-order convergence rate can be achieved with nonsmooth data. Based on the idea of [{\sc Jin, Li, and Zhou}, SIAM J. Sci. Comput., 39 (2017), A3129--A3152], we provide a detailed convergence analysis for the correction BDF$k$ scheme. The numerical experiments with spectral method are given to illustrate the effectiveness of the presented method. To the best of our knowledge, this is the first proof of the convergence analysis and numerical verified the sapce fractional evolution equation with correction BDF$k$.
