In this work, we present the correction schemes of the k-step BDF convolution quadrature at the starting \(k-1\) steps for the fractional Feynman–Kac equation with Lévy flight. Based on the idea of Jin et al. (SIAM J Sci Comput 39:A3129–A3152, 2017), we provide a detailed kth-order convergence analysis for the correction BDFk with nonsmooth data. The numerical experiments with spectral method are given to illustrate theoretical results. Moreover, some simulations and corresponding theoretical for the correction BDFk of the multi-term time fractional model are extended.

中文翻译：

---

带有费利飞行的分数Feynman-Kac方程对高阶BDF卷积正交的校正

在这项工作中，我们提出的校正方案的ķ -step BDF卷积正交在起始\（K-1 \）的分数费曼-KAC方程莱维飞行步骤。基于Jin等人的想法。（SIAM J Sci Comput 39：A3129–A3152，2017年），我们为具有不平滑数据的校正BDF k提供了详细的k阶收敛分析。给出了用频谱方法进行的数值实验，以说明理论结果。此外，扩展了用于多项时间分数模型的校正BDF k的一些模拟和相应的理论。