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High-order numerical approximation formulas for Riemann-Liouville (Riesz) tempered fractional derivatives: construction and application (I)

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  • Zhang, Yuxin
  • Li, Qian
  • Ding, Hengfei

Abstract

In this paper, we develop a new numerical algorithm for solving the Riesz tempered space fractional diffusion equation. The stability and convergence of the numerical scheme are discussed via the technique of matrix analysis. Finally, numerical experiments are performed to confirm the effectiveness of our numerical algorithm.

Suggested Citation

  • Zhang, Yuxin & Li, Qian & Ding, Hengfei, 2018. "High-order numerical approximation formulas for Riemann-Liouville (Riesz) tempered fractional derivatives: construction and application (I)," Applied Mathematics and Computation, Elsevier, vol. 329(C), pages 432-443.
    • Handle: RePEc:eee:apmaco:v:329:y:2018:i:c:p:432-443
    DOI: 10.1016/j.amc.2018.02.023
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    References listed on IDEAS

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    1. Sokolov, I.M & Chechkin, A.V & Klafter, J, 2004. "Fractional diffusion equation for a power-law-truncated Lévy process," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 336(3), pages 245-251.
    2. Sun, HongGuang & Li, Zhipeng & Zhang, Yong & Chen, Wen, 2017. "Fractional and fractal derivative models for transient anomalous diffusion: Model comparison," Chaos, Solitons & Fractals, Elsevier, vol. 102(C), pages 346-353.
    3. Alvaro Cartea & Diego del-Castillo-Negrete, 2007. "On the Fluid Limit of the Continuous-Time Random Walk with General Lévy Jump Distribution Functions," Birkbeck Working Papers in Economics and Finance 0708, Birkbeck, Department of Economics, Mathematics & Statistics.
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    Cited by:

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    2. dos Santos, Maike A.F., 2019. "Analytic approaches of the anomalous diffusion: A review," Chaos, Solitons & Fractals, Elsevier, vol. 124(C), pages 86-96.

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