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Finite Difference Schemes with Non-uniform Time Meshes for Distributed-Order Diffusion Equations

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Proceedings of the International Conference on Fractional Differentiation and its Applications (ICFDA’21) (ICFDA 2021)

Part of the book series: Lecture Notes in Networks and Systems ((LNNS,volume 452))

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Abstract

In this work, a stable and convergent numerical scheme on non-uniform time meshes is proposed, for the solution of distributed-order diffusion equations. A set of numerical results illustrates that the use of particular non-uniform time meshes provides more accurate results than the use of a uniform mesh, in the case of non-smooth solutions.

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Aknowledgments

The first author acknowledges Fundação para a Ciência e Tecnologia within projects UIDB/04621/2020 and UIDP/04621/2020.

This work was also funded by national funds through the FCT - Fundação para a Ciência e a Tecnologia, I.P., under the scope of the project UIDB/00297/2020 (Center for Mathematics and Applications), and, through projects UIDB/00013/2020 and UIDP/00013/2020 (CMAT - Centre of Mathematics - University of Minho).

Author information

Authors and Affiliations

  1. Department of Mathematics, University of Trás-os-Montes and Alto Douro, Vila Real, and Center for Computational and Stochastic Mathematics, Instituto Superior Técnico, Lisboa, Portugal

    M. L. Morgado

  2. Center for Mathematics and Applications (CMA) and Department of Mathematics, FCT NOVA, Lisboa, Portugal

    M. Rebelo

  3. Department of Mechanical Engineering - FEUP, University of Porto & CMAT - Centre of Mathematics, University of Minho, Braga, Portugal

    L. L. Ferrás

Authors
  1. M. L. Morgado
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  2. M. Rebelo
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  3. L. L. Ferrás
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Corresponding author

Correspondence to M. Rebelo .

Editor information

Editors and Affiliations

  1. Institute of Control and Industrial Electronics, Warsaw University Technology, Warsaw, Poland

    Andrzej Dzielinski

  2. Faculty of Electrical Engineering, Institute of Control and Industrial Electronics, Warsaw University of Technology, Warsaw, Poland

    Dominik Sierociuk

  3. Institute of Control and Industrial Electronics, Warsaw University of Technology, Warsaw, Poland

    Piotr Ostalczyk

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Morgado, M.L., Rebelo, M., Ferrás, L.L. (2022). Finite Difference Schemes with Non-uniform Time Meshes for Distributed-Order Diffusion Equations. In: Dzielinski, A., Sierociuk, D., Ostalczyk, P. (eds) Proceedings of the International Conference on Fractional Differentiation and its Applications (ICFDA’21). ICFDA 2021. Lecture Notes in Networks and Systems, vol 452. Springer, Cham. https://doi.org/10.1007/978-3-031-04383-3_27

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