{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,22]],"date-time":"2026-04-22T03:45:52Z","timestamp":1776829552340,"version":"3.51.2"},"reference-count":13,"publisher":"American Mathematical Society (AMS)","issue":"240","license":[{"start":{"date-parts":[[2002,8,3]],"date-time":"2002-08-03T00:00:00Z","timestamp":1028332800000},"content-version":"am","delay-in-days":365,"URL":"https:\/\/www.ams.org\/publications\/copyright-and-permissions"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Comp."],"abstract":"

\n This paper is concerned with the stability of rational one-step approximations of\n \n \n \n \n C<\/mml:mi>\n 0<\/mml:mn>\n <\/mml:msub>\n C_0<\/mml:annotation>\n <\/mml:semantics>\n <\/mml:math>\n <\/inline-formula>\n semigroups. Particular emphasis is laid on long-term stability bounds. The analysis is based on a general Banach space framework and allows variable stepsize sequences. Under reasonable assumptions on the stepsize sequence, asymptotic stability bounds for general\n \n \n \n \n C<\/mml:mi>\n 0<\/mml:mn>\n <\/mml:msub>\n C_0<\/mml:annotation>\n <\/mml:semantics>\n <\/mml:math>\n <\/inline-formula>\n semigroups are derived. The bounds are typical in the sense that they contain, in general, a factor that grows with the number of steps. Under additional hypotheses on the approximation, more favorable stability bounds are obtained for the subclass of holomorphic semigroups.\n <\/p>","DOI":"10.1090\/s0025-5718-01-01389-8","type":"journal-article","created":{"date-parts":[[2002,9,20]],"date-time":"2002-09-20T14:12:48Z","timestamp":1032531168000},"page":"1545-1567","source":"Crossref","is-referenced-by-count":10,"title":["Long-term stability of variable stepsize approximations of semigroups"],"prefix":"10.1090","volume":"71","author":[{"given":"Nikolai","family":"Bakaev","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Alexander","family":"Ostermann","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"14","published-online":{"date-parts":[[2001,8,3]]},"reference":[{"issue":"1","key":"1","first-page":"11","article-title":"Estimates for the stability of a general discretization method","volume":"309","author":"Bakaev, N. 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