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ORIGINAL RESEARCH article

Front. Appl. Math. Stat.
Sec. Mathematical Biology
Volume 10 - 2024 | doi: 10.3389/fams.2024.1358485
This article is part of the Research Topic Modelling and Numerical Simulations with Differential Equations in Mathematical Biology, Medicine and the Environment: Volume II View all 5 articles

Solving a fractional diffusion PDE using some standard and nonstandard finite difference methods with conformable and Caputo operators

Provisionally accepted
Appanah R. Appadu Appanah R. Appadu *Abey S. Kelil Abey S. Kelil Wikocho N. Ndifon Wikocho N. Ndifon
  • Nelson Mandela University, Port Elizabeth, South Africa

The final, formatted version of the article will be published soon.

    Fractional diffusion equations offer an effective means of describing transport phenomena exhibiting abnormal diffusion patterns, often eluding traditional diffusion models. In this paper, we construct four finite difference methods whereby the fractional derivative is approximated using either conformable or Caputo operators and then finite difference approximations are used. To study the stability of the proposed numerical schemes, we employ von Neumann stability analysis or establish conditions under which the schemes replicate/preserve the positivity of the continuous model. Furthermore, consistency analysis is done for all the four methods. Numerical results are presented with fractional parameter (α) set to 0.75, 0.90, 0.95, and 1.0. We also compute the rate of convergence in time for the four methods.

    Keywords: Conformable Derivative, Caputo derivative, Finite difference method, Consistency, stability

    Received: 19 Dec 2023; Accepted: 23 Jul 2024.

    Copyright: © 2024 Appadu, Kelil and Ndifon. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

    * Correspondence: Appanah R. Appadu, Nelson Mandela University, Port Elizabeth, South Africa

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