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Mathematics > Numerical Analysis

arXiv:2006.15876 (math)
[Submitted on 29 Jun 2020]

Title:High-order BDF fully discrete scheme for backward fractional Feynman-Kac equation with nonsmooth data

Authors:Jing Sun, Daxin Nie, Weihua Deng
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Abstract: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.
Comments: 23 pages
Subjects: Numerical Analysis (math.NA)
Cite as: arXiv:2006.15876 [math.NA]
  (or arXiv:2006.15876v1 [math.NA] for this version)
  https://doi.org/10.48550/arXiv.2006.15876
Journal reference: Applied Numerical Mathematics, 161, 82-100, 2021
Related DOI: https://doi.org/10.1016/j.apnum.2020.10.027

Submission history

From: Weihua Deng Professor [view email]
[v1] Mon, 29 Jun 2020 08:59:42 UTC (56 KB)
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