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A block‐centered finite difference method for fractional Cattaneo equation
Author(s) -
Li Xiaoli,
Rui Hongxing,
Liu Zhengguang
Publication year - 2018
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.22198
Subject(s) - mathematics , convergence (economics) , norm (philosophy) , block (permutation group theory) , a priori and a posteriori , stability (learning theory) , finite difference scheme , finite difference , scheme (mathematics) , finite difference method , mathematical analysis , finite element method , geometry , computer science , law , philosophy , epistemology , machine learning , political science , economics , economic growth , physics , thermodynamics
In this article, a block‐centered finite difference method for fractional Cattaneo equation is introduced and analyzed. The unconditional stability and the global convergence of the scheme are proved rigorously. Some a priori estimates of discreteL 2norm with optimal order of convergence O ( Δ t 3 − α+ h 2 + k 2 ) both for pressure and velocity are established on nonuniform rectangular grids. Moreover, the applicability and accuracy of the scheme are demonstrated by numerical experiments to support our theoretical analysis.