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A preconditioned implicit difference scheme for semilinear two‐dimensional time–space fractional Fokker–Planck equations
Author(s) -
Zhang Chengjian,
Zhou Yongtao
Publication year - 2021
Publication title -
numerical linear algebra with applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.02
H-Index - 53
eISSN - 1099-1506
pISSN - 1070-5325
DOI - 10.1002/nla.2357
Subject(s) - mathematics , fokker–planck equation , preconditioner , space (punctuation) , convergence (economics) , computation , kronecker product , rate of convergence , residual , acceleration , kronecker delta , mathematical analysis , algorithm , linear system , channel (broadcasting) , partial differential equation , computer science , physics , computer network , quantum mechanics , classical mechanics , economics , economic growth , operating system
Time–space fractional Fokker–Planck equations (TSFFPEs) are a class of very useful models for describing some practical phenomena in statistical physics. In the present article, we focus on the fast computation for semilinear two‐dimensional TSFFPEs. A stable implicit difference scheme with second‐order accuracy in time and space is derived. In order to accelerate the convergence rate of the scheme, a preconditioned strategy combining the Kronecker product splitting preconditioner and the generalized minimal residual method is suggested. Numerical experiments further confirm the theoretical accuracy of the difference scheme and computational advantage of the acceleration scheme.