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A backward euler orthogonal spline collocation method for the time‐fractional F okker– P lanck equation
Author(s) -
Fairweather Graeme,
Zhang Haixiang,
Yang Xuehua,
Xu Da
Publication year - 2015
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.21958
Subject(s) - mathematics , superconvergence , discretization , collocation (remote sensing) , spline (mechanical) , euler method , euler's formula , collocation method , fokker–planck equation , backward euler method , convergence (economics) , orthogonal collocation , mathematical analysis , partial differential equation , stability (learning theory) , differential equation , finite element method , ordinary differential equation , physics , computer science , machine learning , economic growth , economics , thermodynamics
We formulate and analyze a novel numerical method for solving a time‐fractional Fokker–Planck equation which models an anomalous subdiffusion process. In this method, orthogonal spline collocation is used for the spatial discretization and the time‐stepping is done using a backward Euler method based on the L1 approximation to the Caputo derivative. The stability and convergence of the method are considered, and the theoretical results are supported by numerical examples, which also exhibit superconvergence. © 2014 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 31: 1534–1550, 2015