Correction of BDFk for fractional Feynman-Kac equation with Lévy flight

07/03/2020

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by   Jiankang Shi, et al.

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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 kth-order convergence rate can be achieved with nonsmooth data. Based on the idea of [Jin, Li, and Zhou, SIAM J. Sci. Comput., 39 (2017), A3129–A3152], we provide a detailed convergence analysis for the correction BDFk 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 BDFk.