Correction of high-order BDF convolution quadrature for fractional Feynman-Kac equation with Lévy flight. (English) Zbl 1480.76088
Summary: 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 B. Jin et al. [SIAM J. Sci. Comput. 39, No. 6, A3129–A3152 (2017; Zbl 1379.65078)], we provide a detailed \(k\) th-order convergence analysis for the correction BDF \(k\) with nonsmooth data. The numerical experiments with spectral method are given to illustrate theoretical results. Moreover, some simulations and corresponding theoretical for the correction BDF \(k\) of the multi-term time fractional model are extended.
MSC:
| 76M22 | Spectral methods applied to problems in fluid mechanics |
| 76R99 | Diffusion and convection |
| 26A33 | Fractional derivatives and integrals |
Keywords:
fractional Feynman-Kac equation; Lévy flight; multi-term time-fractional model; fractional substantial derivative; error estimate; spectral methodCitations:
Zbl 1379.65078References:
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