{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,4]],"date-time":"2025-11-04T23:44:30Z","timestamp":1762299870984,"version":"build-2065373602"},"reference-count":20,"publisher":"MDPI AG","issue":"16","license":[{"start":{"date-parts":[[2021,8,18]],"date-time":"2021-08-18T00:00:00Z","timestamp":1629244800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001871","name":"Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia","doi-asserted-by":"publisher","award":["UIDB\/04621\/2020, UIDP\/04621\/2020, UIDB\/00297\/2020, UIDB\/00013\/2020, UIDP\/00013\/2020"],"award-info":[{"award-number":["UIDB\/04621\/2020, UIDP\/04621\/2020, UIDB\/00297\/2020, UIDB\/00013\/2020, UIDP\/00013\/2020"]}],"id":[{"id":"10.13039\/501100001871","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Mathematics"],"abstract":"<jats:p>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.<\/jats:p>","DOI":"10.3390\/math9161975","type":"journal-article","created":{"date-parts":[[2021,8,18]],"date-time":"2021-08-18T10:54:35Z","timestamp":1629284075000},"page":"1975","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Stable and Convergent Finite Difference Schemes on NonuniformTime Meshes for Distributed-Order Diffusion Equations"],"prefix":"10.3390","volume":"9","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5004-6101","authenticated-orcid":false,"given":"M. Lu\u00edsa","family":"Morgado","sequence":"first","affiliation":[{"name":"Center for Computational and Stochastic Mathematics, Instituto Superior T\u00e9cnico, University of Lisbon, 1049-001 Lisbon, Portugal"},{"name":"Department of Mathematics, University of Tr\u00e1s-os-Montes e Alto Douro, UTAD, 5001-801 Vila Real, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4115-3516","authenticated-orcid":false,"given":"Magda","family":"Rebelo","sequence":"additional","affiliation":[{"name":"Center for Mathematics and Applications (CMA), Department of Mathematics, NOVA School of Science and Technology, FCT NOVA, Quinta da Torre, 2829-516 Caparica, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5477-3226","authenticated-orcid":false,"given":"Lu\u00eds L.","family":"Ferr\u00e1s","sequence":"additional","affiliation":[{"name":"Center of Mathematics (CMAT), University of Minho, Campus de Azur\u00e9m, 4800-058 Guimar\u00e3es, Portugal"}]}],"member":"1968","published-online":{"date-parts":[[2021,8,18]]},"reference":[{"key":"ref_1","unstructured":"Caputo, M. 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