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Stable and Convergent Finite Difference Schemes on NonuniformTime Meshes for Distributed-Order Diffusion Equations

Author

Listed:
  • M. Luísa Morgado

    (Center for Computational and Stochastic Mathematics, Instituto Superior Técnico, University of Lisbon, 1049-001 Lisbon, Portugal
    Department of Mathematics, University of Trás-os-Montes e Alto Douro, UTAD, 5001-801 Vila Real, Portugal)

  • Magda Rebelo

    (Center for Mathematics and Applications (CMA), Department of Mathematics, NOVA School of Science and Technology, FCT NOVA, Quinta da Torre, 2829-516 Caparica, Portugal)

  • Luís L. Ferrás

    (Center of Mathematics (CMAT), University of Minho, Campus de Azurém, 4800-058 Guimarães, Portugal)

Abstract

In this work, stable and convergent numerical schemes on nonuniform time meshes are proposed, for the solution of distributed-order diffusion equations. The stability and convergence of the numerical methods are proven, and a set of numerical results illustrate that the use of particular nonuniform time meshes provides more accurate results than the use of a uniform mesh, in the case of nonsmooth solutions.

Suggested Citation

  • M. Luísa Morgado & Magda Rebelo & Luís L. Ferrás, 2021. "Stable and Convergent Finite Difference Schemes on NonuniformTime Meshes for Distributed-Order Diffusion Equations," Mathematics, MDPI, vol. 9(16), pages 1-15, August.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:16:p:1975-:d:616897
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    References listed on IDEAS

    as
    1. X. Wang & F. Liu & X. Chen, 2015. "Novel Second-Order Accurate Implicit Numerical Methods for the Riesz Space Distributed-Order Advection-Dispersion Equations," Advances in Mathematical Physics, Hindawi, vol. 2015, pages 1-14, November.
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