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Second order scheme for self-similar solutions of a time-fractional porous medium equation on the half-line

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  • Okrasińska-Płociniczak, Hanna
  • Płociniczak, Łukasz

Abstract

Many physical, biological, and economical systems exhibit various memory effects due to which their present state depends on the history of the whole evolution. Combined with the nonlinearity of the process these phenomena pose serious difficulties in both analytical and numerical treatment. We investigate a time-fractional porous medium equation that has proved to be important in many applications, notably in hydrology and material sciences. We show that solutions of the free boundary Dirichlet, Neumann, and Robin problems on the half-line satisfy a Volterra integral equation with a non-Lipschitz nonlinearity. Based on this result we prove existence, uniqueness, and construct a family of numerical methods that solve these equations outperforming the usual finite difference approach. Moreover, we prove the convergence of these methods and support the theory with several numerical examples.

Suggested Citation

  • Okrasińska-Płociniczak, Hanna & Płociniczak, Łukasz, 2022. "Second order scheme for self-similar solutions of a time-fractional porous medium equation on the half-line," Applied Mathematics and Computation, Elsevier, vol. 424(C).
    • Handle: RePEc:eee:apmaco:v:424:y:2022:i:c:s0096300322001199
    DOI: 10.1016/j.amc.2022.127033
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    References listed on IDEAS

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    1. Titiwat Sungkaworn & Marie-Lise Jobin & Krzysztof Burnecki & Aleksander Weron & Martin J. Lohse & Davide Calebiro, 2017. "Single-molecule imaging reveals receptor–G protein interactions at cell surface hot spots," Nature, Nature, vol. 550(7677), pages 543-547, October.
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