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

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  • Liu, Zhengguang
  • Cheng, Aijie
  • Li, Xiaoli

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.

Suggested Citation

  • Liu, Zhengguang & Cheng, Aijie & Li, Xiaoli, 2017. "A second order Crank–Nicolson scheme for fractional Cattaneo equation based on new fractional derivative," Applied Mathematics and Computation, Elsevier, vol. 311(C), pages 361-374.
    • Handle: RePEc:eee:apmaco:v:311:y:2017:i:c:p:361-374
    DOI: 10.1016/j.amc.2017.05.032
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    References listed on IDEAS

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    1. Qi, Haitao & Jiang, Xiaoyun, 2011. "Solutions of the space-time fractional Cattaneo diffusion equation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(11), pages 1876-1883.
    2. Atangana, Abdon, 2016. "On the new fractional derivative and application to nonlinear Fisher’s reaction–diffusion equation," Applied Mathematics and Computation, Elsevier, vol. 273(C), pages 948-956.
    3. Gómez-Aguilar, J.F. & López-López, M.G. & Alvarado-Martínez, V.M. & Reyes-Reyes, J. & Adam-Medina, M., 2016. "Modeling diffusive transport with a fractional derivative without singular kernel," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 447(C), pages 467-481.
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