{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,22]],"date-time":"2026-04-22T06:11:17Z","timestamp":1776838277286,"version":"3.51.2"},"reference-count":0,"publisher":"Walter de Gruyter GmbH","issue":"1","license":[{"start":{"date-parts":[[2009,1,1]],"date-time":"2009-01-01T00:00:00Z","timestamp":1230768000000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by-nc-nd\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Comput. Methods Appl. Math."],"published-print":{"date-parts":[[2009]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p> The time discretisation of the initial-value problem for a first-order evolution\nequation by the two-step backward differentiation formula (BDF) on a uniform\ngrid is analysed. The evolution equation is governed by a time-dependent monotone\noperator that might be perturbed by a time-dependent strongly continuous operator.\nWell-posedness of the numerical scheme, a priori estimates, convergence of a piecewise\npolynomial prolongation, stability as well as smooth-data error estimates are provided\nrelying essentially on an algebraic relation that implies the G-stability of the two-step\nBDF with constant time steps.<\/jats:p>","DOI":"10.2478\/cmam-2009-0003","type":"journal-article","created":{"date-parts":[[2013,2,15]],"date-time":"2013-02-15T09:05:50Z","timestamp":1360919150000},"page":"37-62","source":"Crossref","is-referenced-by-count":26,"title":["Two-step Bdf Time Discretisation of Nonlinear Evolution Problems Governed by Monotone Operators with Strongly Continuous Perturbations"],"prefix":"10.2478","volume":"9","author":[{"given":"E.","family":"Emmrich","sequence":"first","affiliation":[{"name":"1TU Berlin, Institut f\u00fcr Mathematik, Stra\u00dfe des 17. Juni 136, 10623 Berlin, Germany."}]}],"member":"374","container-title":["Computational Methods in Applied Mathematics"],"original-title":[],"link":[{"URL":"https:\/\/www.degruyter.com\/view\/journals\/cmam\/9\/1\/article-p37.xml","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.2478\/cmam-2009-0003\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,4,22]],"date-time":"2021-04-22T14:21:21Z","timestamp":1619101281000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.degruyter.com\/view\/journals\/cmam\/9\/1\/article-p37.xml"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009]]},"references-count":0,"journal-issue":{"issue":"1"},"URL":"https:\/\/doi.org\/10.2478\/cmam-2009-0003","relation":{},"ISSN":["1609-9389","1609-4840"],"issn-type":[{"value":"1609-9389","type":"electronic"},{"value":"1609-4840","type":"print"}],"subject":[],"published":{"date-parts":[[2009]]}}}