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Second-order explicit difference schemes for the space fractional advection diffusion equation

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  • Li, Wei
  • Li, Can

Abstract

In this paper, two kinds of explicit second order difference schemes are developed to solve the space fractional advection diffusion equation. The discretizations of fractional derivatives are based on the weighted and shifted Grünwald difference operators developed in [Meerschaert and Tadjeran, J.Comput.Appl.Math. 172 (2004) 65–77; Tian et al., arXiv:1201.5949; Li and Deng, arXiv:1310.7671]. The stability of the presented difference schemes are discussed by means of von Neumann analysis. The analysis shows that the presented numerical schemes are both conditionally stable. The necessary conditions of stability is discussed. Finally, the results of numerical experiments are given to illustrate the performance of the presented numerical methods.

Suggested Citation

  • Li, Wei & Li, Can, 2015. "Second-order explicit difference schemes for the space fractional advection diffusion equation," Applied Mathematics and Computation, Elsevier, vol. 257(C), pages 446-457.
    • Handle: RePEc:eee:apmaco:v:257:y:2015:i:c:p:446-457
    DOI: 10.1016/j.amc.2014.11.030
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    Cited by:

    1. Chang, Ailian & Sun, HongGuang & Zheng, Chunmiao & Lu, Bingqing & Lu, Chengpeng & Ma, Rui & Zhang, Yong, 2018. "A time fractional convection–diffusion equation to model gas transport through heterogeneous soil and gas reservoirs," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 502(C), pages 356-369.
    2. Saberi Zafarghandi, Fahimeh & Mohammadi, Maryam & Babolian, Esmail & Javadi, Shahnam, 2019. "Radial basis functions method for solving the fractional diffusion equations," Applied Mathematics and Computation, Elsevier, vol. 342(C), pages 224-246.
    3. Nyamoradi, Nemat & Rodríguez-López, Rosana, 2015. "On boundary value problems for impulsive fractional differential equations," Applied Mathematics and Computation, Elsevier, vol. 271(C), pages 874-892.

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