论文标题
高阶BDF完全离散的方案，用于带有非平滑数据的向后分数Feynman-kac方程
High-order BDF fully discrete scheme for backward fractional Feynman-Kac equation with nonsmooth data
论文作者
论文摘要
Feynman-KAC方程控制了可观察到的统计分布 - 功能，在几乎所有学科中都具有广泛的应用。在克服了时间空间耦合的非局部运算符和可能的低规律性的挑战之后，本文通过使用向后差公式（BDF）卷积方程式在空间中，有限的元素方法以及一些校正术语来开发用于向后分数FEYNMAN-KAC方程的高级完全离散方案。通过系统的校正，高收敛顺序的时间最高可达$ 6 $，而不会降低空间中最佳的收敛性，并且没有解决方案的规律性要求。最后，广泛的数值实验验证了高阶方案的有效性。
The Feynman-Kac equation governs the distribution of the statistical observable -- functional, having wide applications in almost all disciplines. After overcoming challenges from the time-space coupled nonlocal operator and the possible low regularity of functional, this paper develops the high-order fully discrete scheme for the backward fractional Feynman-Kac equation by using backward difference formulas (BDF) convolution quadrature in time, finite element method in space, and some correction terms. With a systematic correction, the high convergence order is achieved up to $6$ in time, without deteriorating the optimal convergence in space and without the regularity requirement on the solution. Finally, the extensive numerical experiments validate the effectiveness of the high-order schemes.
