{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,22]],"date-time":"2026-04-22T07:15:32Z","timestamp":1776842132734,"version":"3.51.2"},"reference-count":11,"publisher":"American Mathematical Society (AMS)","issue":"246","license":[{"start":{"date-parts":[[2004,6,19]],"date-time":"2004-06-19T00:00:00Z","timestamp":1087603200000},"content-version":"am","delay-in-days":366,"URL":"https:\/\/www.ams.org\/publications\/copyright-and-permissions"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Comp."],"abstract":"<p>We construct and analyze combinations of rational implicit and explicit multistep methods for nonlinear parabolic equations. The resulting schemes are linearly implicit and include as particular cases implicit-explicit multistep schemes as well as the combination of implicit Runge-Kutta schemes and extrapolation. An optimal condition for the stability constant is derived under which the schemes are locally stable. We establish optimal order error estimates.<\/p>","DOI":"10.1090\/s0025-5718-03-01573-4","type":"journal-article","created":{"date-parts":[[2004,4,21]],"date-time":"2004-04-21T12:29:08Z","timestamp":1082550548000},"page":"613-635","source":"Crossref","is-referenced-by-count":40,"title":["Linearly implicit methods for nonlinear parabolic equations"],"prefix":"10.1090","volume":"73","author":[{"given":"Georgios","family":"Akrivis","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Michel","family":"Crouzeix","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"14","published-online":{"date-parts":[[2003,6,19]]},"reference":[{"key":"1","first-page":"635","article-title":"A mean ergodic theorem","volume":"5","author":"Dunford, Nelson","year":"1939","journal-title":"Duke Math. 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Th\u00e8se, Universit\u00e9 de Paris VI, 1975."},{"issue":"2","key":"5","doi-asserted-by":"publisher","first-page":"394","DOI":"10.1137\/0727024","article-title":"Galerkin\/Runge-Kutta discretizations for semilinear parabolic equations","volume":"27","author":"Keeling, Stephen L.","year":"1990","journal-title":"SIAM J. Numer. 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(2)","ISSN":"https:\/\/id.crossref.org\/issn\/0003-486X","issn-type":"print"},{"key":"11","series-title":"Lecture Notes in Mathematics","isbn-type":"print","volume-title":"Galerkin finite element methods for parabolic problems","volume":"1054","author":"Thom\u00e9e, Vidar","year":"1984","ISBN":"https:\/\/id.crossref.org\/isbn\/3540129111"}],"container-title":["Mathematics of Computation"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/www.ams.org\/mcom\/2004-73-246\/S0025-5718-03-01573-4\/S0025-5718-03-01573-4.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"},{"URL":"https:\/\/www.ams.org\/mcom\/2004-73-246\/S0025-5718-03-01573-4\/S0025-5718-03-01573-4.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,21]],"date-time":"2026-04-21T13:43:46Z","timestamp":1776779026000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.ams.org\/mcom\/2004-73-246\/S0025-5718-03-01573-4\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2003,6,19]]},"references-count":11,"journal-issue":{"issue":"246","published-print":{"date-parts":[[2004,4]]}},"alternative-id":["S0025-5718-03-01573-4"],"URL":"https:\/\/doi.org\/10.1090\/s0025-5718-03-01573-4","archive":["CLOCKSS","Portico"],"relation":{},"ISSN":["1088-6842","0025-5718"],"issn-type":[{"value":"1088-6842","type":"electronic"},{"value":"0025-5718","type":"print"}],"subject":[],"published":{"date-parts":[[2003,6,19]]}}}