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

M. Luísa Morgado, Magda Rebelo and Luís L. Ferrás
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M. Luísa Morgado: Center for Computational and Stochastic Mathematics, Instituto Superior Técnico, University of Lisbon, 1049-001 Lisbon, 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

Mathematics, 2021, vol. 9, issue 16, 1-15

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.

Keywords: distributed-order derivatives; finite differences; diffusion equations; nonuniform meshes; stability; convergence (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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