{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T18:34:00Z","timestamp":1787337240901,"version":"build-2736575974"},"reference-count":21,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"5","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Sci. Comput."],"published-print":{"date-parts":[[2001,1]]},"abstract":"<jats:p>Iterated deferred correction is a widely used approach to the numerical solution of first order systems of nonlinear two-point boundary value problems. Normally the orders of accuracy of the various methods used in a deferred correction scheme differ by 2, and, as a direct result, each time a deferred correction is applied the order of the overall scheme is increased by a maximum of 2. In this paper we consider the construction of mono-implicit Runge--Kutta (MIRK) methods where an increase of four orders of accuracy is obtained for each deferred correction. We develop a very powerful yet rather straightforward theory which allows us to identify the appropriate Runge--Kutta formulae for inclusion in such schemes. In particular, we will focus on the construction of pairs of MIRK formulae of order 4 and 8 which will allow this superconvergence to be realized. We will further show that it is possible to derive formulae of this type for which high order interpolants and accurate error estimates are readily available.<\/jats:p>","DOI":"10.1137\/s1064827599362004","type":"journal-article","created":{"date-parts":[[2003,6,11]],"date-time":"2003-06-11T11:12:06Z","timestamp":1055329926000},"page":"1697-1716","source":"Crossref","is-referenced-by-count":5,"title":["Superconvergent Deferred Correction Methods For First Order Systems of Nonlinear Two-Point Boundary Value Problems"],"prefix":"10.1137","volume":"22","author":[{"given":"Marnix","family":"Van Daele","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jeff R.","family":"Cash","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2006,7,25]]},"reference":[{"key":"R1","doi-asserted-by":"publisher","DOI":"10.1016\/S0898-1221(98)80009-6"},{"key":"R2","doi-asserted-by":"publisher","DOI":"10.1007\/BF01933583"},{"key":"R3","doi-asserted-by":"publisher","DOI":"10.1137\/0731047"},{"key":"R4","unstructured":"J. C. Butcher,\n                      The Numerical Analysis of Ordinary Differential Equations: Runge\u2013Kutta and General Linear Methods\n                      , Wiley, Chichester, UK, 1987."},{"key":"R5","doi-asserted-by":"publisher","DOI":"10.1016\/0898-1221(83)90129-3"},{"key":"R6","first-page":"55","volume":"15","author":"Cash J.","year":"1996","journal-title":"Mat. Apl. Comput."},{"key":"R7","doi-asserted-by":"publisher","DOI":"10.1137\/0725049"},{"key":"R8","doi-asserted-by":"publisher","DOI":"10.1137\/0912052"},{"key":"R9","doi-asserted-by":"publisher","DOI":"10.1006\/jcph.1995.1212"},{"key":"R10","doi-asserted-by":"publisher","DOI":"10.1145\/321906.321915"},{"key":"R11","doi-asserted-by":"publisher","DOI":"10.1007\/BF01944476"},{"key":"R12","doi-asserted-by":"publisher","DOI":"10.1093\/imanum\/2.2.211"},{"key":"R13","doi-asserted-by":"publisher","DOI":"10.1007\/BF02251090"},{"key":"R14","volume-title":"Solving ordinary differential equations. I","author":"Hairer E.","year":"1993"},{"key":"R15","unstructured":"P. W. Hemker,\n                      A Numerical Study of Stiff Two\u2010Point Boundary Value Problems\n                      , Mathematisch Centrum, Amsterdam, 1977."},{"key":"R16","doi-asserted-by":"publisher","DOI":"10.1137\/0714006"},{"key":"R17","unstructured":"J. D. Lambert,\n                      Computational Methods in Ordinary Differential Equations\n                      , Wiley, London, 1973."},{"key":"R18","doi-asserted-by":"publisher","DOI":"10.1007\/BF01385631"},{"key":"R19","doi-asserted-by":"publisher","DOI":"10.1137\/0719009"},{"key":"R20","doi-asserted-by":"publisher","DOI":"10.1016\/S0377-0427(99)00130-2"},{"key":"R21","unstructured":"T. Van Hecke,\n                      Mono\u2010impliciete Runge\u2010Kutta(\u2010Nystr\u00f6m) methodes\n                      , Ph.D. thesis, University of Ghent, Ghent, Belgium, 1998."}],"container-title":["SIAM Journal on Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/S1064827599362004","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T17:51:48Z","timestamp":1787334708000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/S1064827599362004"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2001,1]]},"references-count":21,"journal-issue":{"issue":"5","published-print":{"date-parts":[[2001,1]]}},"alternative-id":["10.1137\/S1064827599362004"],"URL":"https:\/\/doi.org\/10.1137\/s1064827599362004","relation":{},"ISSN":["1064-8275","1095-7197"],"issn-type":[{"value":"1064-8275","type":"print"},{"value":"1095-7197","type":"electronic"}],"subject":[],"published":{"date-parts":[[2001,1]]}}}