2017
DOI: 10.1002/num.22198
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A block‐centered finite difference method for fractional Cattaneo equation

Abstract: 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 discrete L 2 norm with optimal order of convergenceboth 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.

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Cited by 4 publications
(4 citation statements)
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References 37 publications
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“…For comparison, we also test the second-order in space fast L1-BCFD method for model (1.1) (4.4). This scheme can be derived similarly as [51] for the time-fractional diffusion equation or [23] for the time-fractional Cattaneo equation.…”
Section: Numerical Resultsmentioning
confidence: 99%
See 2 more Smart Citations
“…For comparison, we also test the second-order in space fast L1-BCFD method for model (1.1) (4.4). This scheme can be derived similarly as [51] for the time-fractional diffusion equation or [23] for the time-fractional Cattaneo equation.…”
Section: Numerical Resultsmentioning
confidence: 99%
“…Besides, the BCFD method can guarantee the mass conservation and result in a symmetric positive definite system, compared with a saddle-point system generated by the classical mixed element method [34]. Therefore, the BCFD method is more efficient and widely used for modeling of flow model [37,58], convection-diffusion model [52], and even time-fractional model [17,22,23,51]. Recently, Shi et al [40] proposed a compact BCFD method for the elliptic and parabolic problems, which further improves the spatial accuracy from second-order to fourth-order.…”
Section: Introductionmentioning
confidence: 99%
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“…Caputo and Fabrizio proposed one of the most recent fractional order derivatives. For more applications of this new derivative and the related work, the reader is referred to [1,[16][17][18][19][20][21][22][23][24][25][26][27][28][29].…”
Section: Introductionmentioning
confidence: 99%