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arXiv · 2305.06880

Analysis of a WSGD scheme for backward fractional Feynman-Kac equation with nonsmooth data

Liyao Hao·Wenyi Tian
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Abstract

In this paper, we propose and analyze a second-order time-stepping numerical scheme for the inhomogeneous backward fractional Feynman-Kac equation with nonsmooth initial data. The complex parameters and time-space coupled Riemann-Liouville fractional substantial integral and derivative in the equation bring challenges on numerical analysis and computations. The nonlocal operators are approximated by using the weighted and shifted Gr\"{u}nwald difference (WSGD) formula. Then a second-order WSGD scheme is obtained after making some initial corrections. Moreover, the error estimates of the proposed time-stepping scheme are rigorously established without the regularity requirement on the exact solution. Finally, some numerical experiments are performed to validate the efficiency and accuracy of the proposed numerical scheme.

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Liyao Hao, Wenyi Tian. 2023-05-11. Analysis of a WSGD scheme for backward fractional Feynman-Kac equation with nonsmooth data. https://doi.org/10.1007/s10444-024-10188-7

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