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Numer. Anal."],"published-print":{"date-parts":[[2019,1]]},"abstract":"<jats:p>We present a numerical method for convergence acceleration for multifidelity models of parameterized ordinary differential equations. The hierarchy of models is defined as trajectories computed using different timesteps in a time integration scheme. Our first contribution is in novel analysis of the multifidelity procedure, providing a convergence estimate. Our second contribution is development of a three-step algorithm that uses multifidelity surrogates to accelerate convergence: step one uses a multifidelity procedure at three levels to obtain accurate predictions using inexpensive (large timestep) models. Step two uses high-order splines to construct continuous trajectories over time. Finally, step three combines spline predictions at three levels to infer an order of convergence and compute a sequence transformation prediction (in particular we use Richardson extrapolation) that achieves superior error. We demonstrate our procedure on linear and nonlinear systems of parameterized ordinary differential equations.<\/jats:p>","DOI":"10.1137\/18m1170339","type":"journal-article","created":{"date-parts":[[2019,6,13]],"date-time":"2019-06-13T11:39:49Z","timestamp":1560425989000},"page":"1344-1368","source":"Crossref","is-referenced-by-count":3,"title":["Convergence Acceleration for Time-Dependent Parametric Multifidelity Models"],"prefix":"10.1137","volume":"57","author":[{"given":"Vahid","family":"Keshavarzzadeh","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Robert M.","family":"Kirby","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5914-4207","authenticated-orcid":true,"given":"Akil","family":"Narayan","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2019,6,13]]},"reference":[{"key":"atypb1","doi-asserted-by":"publisher","DOI":"10.1016\/j.wavemoti.2010.03.005"},{"key":"atypb2","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4471-5102-9_142-1"},{"key":"atypb3","doi-asserted-by":"publisher","DOI":"10.1137\/130932715"},{"key":"atypb4","doi-asserted-by":"publisher","DOI":"10.1137\/100795772"},{"key":"atypb5","doi-asserted-by":"publisher","DOI":"10.1016\/0168-9274(95)00110-7"},{"key":"atypb6","doi-asserted-by":"publisher","DOI":"10.1016\/S0377-0427(00)00360-5"},{"key":"atypb7","doi-asserted-by":"publisher","DOI":"10.1002\/nme.3050"},{"key":"atypb8","doi-asserted-by":"publisher","DOI":"10.1007\/s00365-013-9186-2"},{"key":"atypb9","volume-title":"Solving Ordinary Differential Equations I: Nonstiff Problems","author":"Hairer E.","year":"1993"},{"key":"atypb11","doi-asserted-by":"publisher","DOI":"10.1016\/j.jeconom.2007.12.004"},{"key":"atypb12","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-22470-1"},{"key":"atypb13","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9780511622700","volume-title":"Coherent Structures, Dynamical Systems and Symmetry","author":"Holmes P.","year":"1996"},{"key":"atypb14","doi-asserted-by":"publisher","DOI":"10.1137\/0720036"},{"key":"atypb15","doi-asserted-by":"publisher","DOI":"10.1137\/1013092"},{"key":"atypb16","doi-asserted-by":"publisher","DOI":"10.1137\/17M1137875"},{"key":"atypb17","doi-asserted-by":"publisher","DOI":"10.1007\/s10915-016-0331-5"},{"key":"atypb18","doi-asserted-by":"publisher","DOI":"10.1007\/978-88-470-2592-9_16"},{"key":"atypb19","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmps.2011.09.002"},{"key":"atypb20","doi-asserted-by":"publisher","DOI":"10.1023\/A:1015145924517"},{"key":"atypb21","doi-asserted-by":"publisher","DOI":"10.1137\/130929461"},{"key":"atypb22","doi-asserted-by":"publisher","DOI":"10.1007\/BF01397089"},{"key":"atypb23","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-15431-2"},{"key":"atypb24","doi-asserted-by":"publisher","DOI":"10.1137\/S1064827594276424"},{"key":"atypb25","doi-asserted-by":"publisher","DOI":"10.1007\/BF02165234"},{"key":"atypb26","doi-asserted-by":"publisher","DOI":"10.1016\/0167-7977(89)90011-7"},{"key":"atypb27","doi-asserted-by":"publisher","DOI":"10.1090\/S0025-5718-1986-0815835-1"},{"key":"atypb28","doi-asserted-by":"publisher","DOI":"10.1137\/130949154"}],"container-title":["SIAM Journal on Numerical Analysis"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/18M1170339","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T17:31:02Z","timestamp":1787333462000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/18M1170339"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,1]]},"references-count":27,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2019,1]]}},"alternative-id":["10.1137\/18M1170339"],"URL":"https:\/\/doi.org\/10.1137\/18m1170339","relation":{},"ISSN":["0036-1429","1095-7170"],"issn-type":[{"value":"0036-1429","type":"print"},{"value":"1095-7170","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,1]]}}}