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A novel numerical scheme for a time fractional Black–Scholes equation

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Abstract

This paper consists of two parts. On one hand, the regularity of the solution of the time-fractional Black–Scholes equation is investigated. On the other hand, to overcome the difficulty of initial layer, a modified L1 time discretization is presented based on a change of variable. And the spatial discretization is done by using the Chebyshev Galerkin method. Optimal error estimates of the fully-discrete scheme are obtained. Finally, several numerical results are given to confirm the theoretical results.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan, 430074, China

    Mianfu She, Lili Li, Renxuan Tang & Dongfang Li

  2. Hubei Key Laboratory of Engineering Modeling and Scientific Computing, Huazhong University of Science and Technology, Wuhan, 430074, China

    Mianfu She & Dongfang Li

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  1. Mianfu She
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  2. Lili Li
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  3. Renxuan Tang
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  4. Dongfang Li
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Correspondence to Renxuan Tang.

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This work is supported by NSFC (Grant No.11771162)

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She, M., Li, L., Tang, R. et al. A novel numerical scheme for a time fractional Black–Scholes equation. J. Appl. Math. Comput. 66, 853–870 (2021). https://doi.org/10.1007/s12190-020-01467-9

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  • DOI: https://doi.org/10.1007/s12190-020-01467-9

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