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For these two classes, with up to three additional diagonally-implicit stages, we derive methods that satisfy appropriate order conditions for index-2 DAEs.<\/p>","DOI":"10.1090\/s0025-5718-98-00953-3","type":"journal-article","created":{"date-parts":[[2002,7,26]],"date-time":"2002-07-26T18:14:44Z","timestamp":1027707284000},"page":"1001-1021","source":"Crossref","is-referenced-by-count":7,"title":["Efficient Runge-Kutta integrators for index-2 differential algebraic equations"],"prefix":"10.1090","volume":"67","author":[{"given":"J.","family":"Butcher","sequence":"first","affiliation":[]},{"given":"R.","family":"Chan","sequence":"additional","affiliation":[]}],"member":"14","published-online":{"date-parts":[[1998]]},"reference":[{"key":"1","volume-title":"Handbook of mathematical functions, with formulas, graphs, and mathematical tables","year":"1966"},{"issue":"3","key":"2","doi-asserted-by":"publisher","first-page":"326","DOI":"10.1007\/BF01932774","article-title":"An implementation of singly-implicit Runge-Kutta methods","volume":"20","author":"Burrage, K.","year":"1980","journal-title":"BIT","ISSN":"https:\/\/id.crossref.org\/issn\/0006-3835","issn-type":"print"},{"issue":"1-2","key":"3","doi-asserted-by":"publisher","first-page":"17","DOI":"10.1016\/0377-0427(93)90261-9","article-title":"On smoothing and order reduction effects for implicit Runge-Kutta formulae","volume":"45","author":"Burrage, Kevin","year":"1993","journal-title":"J. Comput. Appl. Math.","ISSN":"https:\/\/id.crossref.org\/issn\/0377-0427","issn-type":"print"},{"key":"4","series-title":"A Wiley-Interscience Publication","isbn-type":"print","volume-title":"The numerical analysis of ordinary differential equations","author":"Butcher, J. C.","year":"1987","ISBN":"https:\/\/id.crossref.org\/isbn\/0471910465"},{"issue":"1","key":"5","doi-asserted-by":"publisher","first-page":"68","DOI":"10.1145\/42288.42341","article-title":"Towards efficient implementation of singly-implicit methods","volume":"14","author":"Butcher, J. C.","year":"1988","journal-title":"ACM Trans. Math. Software","ISSN":"https:\/\/id.crossref.org\/issn\/0098-3500","issn-type":"print"},{"issue":"3","key":"6","doi-asserted-by":"publisher","first-page":"753","DOI":"10.1137\/0727044","article-title":"Towards efficient Runge-Kutta methods for stiff systems","volume":"27","author":"Butcher, J. C.","year":"1990","journal-title":"SIAM J. Numer. Anal.","ISSN":"https:\/\/id.crossref.org\/issn\/0036-1429","issn-type":"print"},{"key":"7","unstructured":"R.P.K. Chan and P. Chartier, Gaussian symmetrizers for index-2 differential algebraic equations (unpublished notes, 1994)."},{"key":"8","doi-asserted-by":"publisher","first-page":"82","DOI":"10.2307\/1989993","article-title":"Maximal orders in rational cyclic algebras of composite degree","volume":"46","author":"Perlis, Sam","year":"1939","journal-title":"Trans. Amer. Math. 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