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An implicit Keller Box numerical scheme for the solution of fractional subdiffusion equations

Author

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  • Osman, S.A.
  • Langlands, T.A.M.

Abstract

In this work, we present a new implicit numerical scheme for fractional subdiffusion equations. In this approach we use the Keller Box method [1] to spatially discretise the fractional subdiffusion equation and we use a modified L1 scheme (ML1), similar to the L1 scheme originally developed by Oldham and Spanier [2], to approximate the fractional derivative. The stability of the proposed method was investigated by using Von-Neumann stability analysis. We have proved the method is unconditionally stable when 0<λq

Suggested Citation

  • Osman, S.A. & Langlands, T.A.M., 2019. "An implicit Keller Box numerical scheme for the solution of fractional subdiffusion equations," Applied Mathematics and Computation, Elsevier, vol. 348(C), pages 609-626.
    • Handle: RePEc:eee:apmaco:v:348:y:2019:i:c:p:609-626
    DOI: 10.1016/j.amc.2018.12.015
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    References listed on IDEAS

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    1. Giona, Massimiliano & Eduardo Roman, H., 1992. "Fractional diffusion equation for transport phenomena in random media," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 185(1), pages 87-97.
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    More about this item

    Keywords

    Fractional subdiffusion equation; Keller Box method; Fractional calculus; L1 scheme; Linear reaction;
    All these keywords.

    JEL classification:

    • L1 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance

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