A second order Crank–Nicolson scheme for fractional Cattaneo equation based on new fractional derivative

Zhengguang Liu, Aijie Cheng and Xiaoli Li

Applied Mathematics and Computation, 2017, vol. 311, issue C, 361-374

Abstract: Recently Caputo and Fabrizio introduce a new derivative with fractional order which has the ability to describe the material heterogeneities and the fluctuations of different scales. In this article, a Crank–Nicolson finite difference scheme to solve fractional Cattaneo equation based on the new fractional derivative is introduced and analyzed. Some a priori estimates of discrete L∞(L2) errors with optimal order of convergence rate O(τ2+h2) are established on uniform partition. Moreover, the applicability and accuracy of the scheme are demonstrated by numerical experiments to support our theoretical analysis.

Keywords: Second order; New fractional derivative; Crank–Nicolson; Cattaneo equation; Finite difference (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:311:y:2017:i:c:p:361-374

DOI: 10.1016/j.amc.2017.05.032

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