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A higher order numerical scheme for generalized fractional diffusion equations
Author(s) -
Ding Qinxu,
Wong Patricia J. Y.
Publication year - 2020
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.4852
Subject(s) - mathematics , convergence (economics) , fractional calculus , stability (learning theory) , order (exchange) , function (biology) , scheme (mathematics) , mittag leffler function , numerical analysis , mathematical analysis , computer science , machine learning , evolutionary biology , economics , biology , economic growth , finance
In this article, we develop a higher order approximation for the generalized fractional derivative that includes a scale function z ( t ) and a weight function w ( t ). This is then used to solve a generalized fractional diffusion problem numerically. The stability and convergence analysis of the numerical scheme are conducted by the energy method. It is proven that the temporal convergence order is 3 and this is the best result to date. Finally, we present four examples to confirm the theoretical results.