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 method of Chang-Cooper for spatial discretization with the Strang-Marchuk splitting and first- and second-order time discretization methods. It is proven that the SIMEX scheme is second-order accurate, positive preserving, and conservative. Results of numerical experiments that validate the theoretical results are presented. (This chapter is a summary of the paper Gaviraghi et al. (Appl Math Comput, 2017); all theoretical statements in this summary are proved in that reference.)
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Gaviraghi, B., Annunziato, M., Borzì, A. (2017). Splitting Methods for Fokker-Planck Equations Related to Jump-Diffusion Processes. In: Ehrhardt, M., Günther, M., ter Maten, E. (eds) Novel Methods in Computational Finance. Mathematics in Industry(), vol 25. Springer, Cham. https://doi.org/10.1007/978-3-319-61282-9_22
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DOI: https://doi.org/10.1007/978-3-319-61282-9_22
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