Approximation of an optimal control problem for the time-fractional Fokker-Planck equation
Type
ArticleKAUST Department
Applied Mathematics and Computational Science ProgramApplied Mathematics & Computational Sci
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Date
2021Preprint Posting Date
2020-06-05Embargo End Date
2022-03-22Permanent link to this record
http://hdl.handle.net/10754/663758
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In this paper, we study the numerical approximation of a system of PDEs which arises from an optimal control problem for the time-fractional Fokker-Planck equation with time-dependent drift. The system is composed of a backward time-fractional Hamilton-Jacobi-Bellman equation and a forward time-fractional Fokker-Planck equation. We approximate Caputo derivatives in the system by means of L1 schemes and the Hamiltonian by finite differences. The scheme for the Fokker-Planck equation is constructed in such a way that the duality structure of the PDE system is preserved on the discrete level. We prove the well-posedness of the scheme and the convergence to the solution of the continuous problem.Citation
Camilli, F., Duisembay, S., & Tang, Q. (2021). Approximation of an optimal control problem for the time-fractional Fokker-Planck equation. Journal of Dynamics & Games, 0(0), 0. doi:10.3934/jdg.2021013Journal
Journal of Dynamics & GamesarXiv
2006.03518Additional Links
https://www.aimsciences.org/article/doi/10.3934/jdg.2021013ae974a485f413a2113503eed53cd6c53
10.3934/jdg.2021013