{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,21]],"date-time":"2026-04-21T15:10:54Z","timestamp":1776784254636,"version":"3.51.2"},"reference-count":14,"publisher":"American Mathematical Society (AMS)","issue":"251","license":[{"start":{"date-parts":[[2005,9,10]],"date-time":"2005-09-10T00:00:00Z","timestamp":1126310400000},"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":"<p>We analyze a single step method for solving second-order parabolic initial\u2013boundary value problems. The method uses a step-doubling extrapolation scheme in time based on backward Euler and a Galerkin approximation in space. The technique is shown to be a second-order correct approximation in time. Since step-doubling can be used as a mechanism for step-size control, the analysis is done for variable time steps. The stability properties of step-doubling are contrasted with those of Crank-Nicolson, as well as those of more general extrapolated theta-weighted schemes. We provide an example computation that illustrates both the use of step-doubling for adaptive time step control and the application of step-doubling to a nonlinear system.<\/p>","DOI":"10.1090\/s0025-5718-04-01696-5","type":"journal-article","created":{"date-parts":[[2005,4,12]],"date-time":"2005-04-12T12:20:25Z","timestamp":1113308425000},"page":"1053-1065","source":"Crossref","is-referenced-by-count":11,"title":["Convergence of a step-doubling Galerkin method for parabolic problems"],"prefix":"10.1090","volume":"74","author":[{"given":"Bruce","family":"Ayati","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Todd","family":"Dupont","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"14","published-online":{"date-parts":[[2004,9,10]]},"reference":[{"key":"1","unstructured":"Bruce P. Ayati, \ud835\udc35\ud835\udc62\ud835\udc3a\ud835\udc46 1.0 user guide, Tech. 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