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Besides the well-definedness of the methods, the global error and superconvergence properties are analyzed under rather weak abstract assumptions which also allow considerations of a wide variety of quadrature formulas. Numerical experiments illustrate and support the theoretical results.<\/jats:p>","DOI":"10.1007\/s11075-021-01164-z","type":"journal-article","created":{"date-parts":[[2021,8,12]],"date-time":"2021-08-12T01:02:15Z","timestamp":1628730135000},"page":"1533-1565","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Unified analysis for variational time discretizations of higher order and higher regularity applied to non-stiff ODEs"],"prefix":"10.1007","volume":"89","author":[{"given":"Simon","family":"Becher","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9476-3740","authenticated-orcid":false,"given":"Gunar","family":"Matthies","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2021,8,12]]},"reference":[{"key":"1164_CR1","doi-asserted-by":"publisher","first-page":"429","DOI":"10.1007\/s00211-011-0363-6","volume":"118","author":"G Akrivis","year":"2011","unstructured":"Akrivis, G., Makridakis, C.H., Nochetto, R.H.: Galerkin and Runge-Kutta methods: unified formulation, a posteriori error estimates and nodal superconvergence. 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