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Analysis of splitting methods for solving a partial integro-differential Fokker–Planck equation

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  • Gaviraghi, B.
  • Annunziato, M.
  • Borzì, A.

Abstract

A splitting implicit-explicit (SIMEX) scheme for solving a partial integro-differential Fokker–Planck equation related to a jump-diffusion process is investigated. This scheme combines the Chang–Cooper method for spatial discretization with the Strang–Marchuk splitting and first- and second-order time discretization methods. It is proved that the SIMEX scheme is second-order accurate, positive preserving, and conservative. Results of numerical experiments that validate the theoretical results are presented.

Suggested Citation

  • Gaviraghi, B. & Annunziato, M. & Borzì, A., 2017. "Analysis of splitting methods for solving a partial integro-differential Fokker–Planck equation," Applied Mathematics and Computation, Elsevier, vol. 294(C), pages 1-17.
    • Handle: RePEc:eee:apmaco:v:294:y:2017:i:c:p:1-17
    DOI: 10.1016/j.amc.2016.08.050
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    References listed on IDEAS

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    1. Rama Cont & Ekaterina Voltchkova, 2005. "Integro-differential equations for option prices in exponential Lévy models," Finance and Stochastics, Springer, vol. 9(3), pages 299-325, July.
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    Cited by:

    1. Olga S. Rozanova & Nikolai A. Krutov, 2024. "The fundamental solution of the master equation for a jump‐diffusion Ornstein–Uhlenbeck process," Mathematische Nachrichten, Wiley Blackwell, vol. 297(8), pages 3052-3063, August.
    2. Zhang, Hui & Jiang, Xiaoyun & Yang, Xiu, 2018. "A time-space spectral method for the time-space fractional Fokker–Planck equation and its inverse problem," Applied Mathematics and Computation, Elsevier, vol. 320(C), pages 302-318.

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