@article{d6997292476d490aaf66b3b2a44f7e48,
title = "Stable and convergent finite difference schemes on nonuniformtime meshes for distributed-order diffusion equations",
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 = "Convergence, Diffusion equations, Distributed-order derivatives, Finite differences, Nonuniform meshes, Stability",
author = "Morgado, {M. Lu{\'i}sa} and Magda Rebelo and Ferr{\'a}s, {Lu{\'i}s L.}",
note = "Funding Information: Acknowledgments: The authors acknowledge the support of the Center for Mathematics and Applications (CMA)—FCT-NOVA, Center for Computational and Stochastic Mathematics, Instituto Superior T{\'e}cnico, and CMAT—Centre of Mathematics—University of Minho. The first author acknowledges Funda{\c c}{\~a}o para a Ci{\^e}ncia e Tecnologia (Portuguese Foundation for Science and Technology) within Projects UIDB/04621/2020 and UIDP/04621/2020. The second author acknowledges the Funda{\c c}{\~a}o para a Ci{\^e}ncia e a Tecnologia through Project UIDB/00297/2020 (Centro de Matem{\'a}tica e Aplica{\c c}{\~o}es). The third author acknowledges the funding by Funda{\c c}{\~a}o para a Ci{\^e}ncia e Tecnologia through Projects UIDB/00013/2020 and UIDP/00013/2020. ",
year = "2021",
month = aug,
day = "18",
doi = "10.3390/math9161975",
language = "English",
volume = "9",
journal = "Mathematics",
publisher = "MDPI - Multidisciplinary Digital Publishing Institute",
number = "16",
}