{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,5,17]],"date-time":"2025-05-17T04:16:14Z","timestamp":1747455374603,"version":"3.40.5"},"reference-count":28,"publisher":"Springer Science and Business Media LLC","issue":"1-2","license":[{"start":{"date-parts":[[1997,3,1]],"date-time":"1997-03-01T00:00:00Z","timestamp":857174400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[1997,3,1]],"date-time":"1997-03-01T00:00:00Z","timestamp":857174400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Advances in Computational Mathematics"],"published-print":{"date-parts":[[1997,3]]},"DOI":"10.1023\/a:1018930415863","type":"journal-article","created":{"date-parts":[[2003,2,19]],"date-time":"2003-02-19T22:07:13Z","timestamp":1045692433000},"page":"37-57","source":"Crossref","is-referenced-by-count":13,"title":["Parallel iterated methods based on multistep Runge-Kutta methods of Radau type"],"prefix":"10.1007","volume":"7","author":[{"given":"K.","family":"Burrage","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"H.","family":"Suhartanto","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","reference":[{"key":"325258_CR1","doi-asserted-by":"crossref","first-page":"452","DOI":"10.1007\/BF01933639","volume":"20","author":"K. Burrage","year":"1980","unstructured":"K. Burrage and P. M. Moss, Simplifying assumptions for the order of partitioned multivalue methods, BIT 20 (1980) 452\u2013465.","journal-title":"BIT"},{"key":"325258_CR2","doi-asserted-by":"crossref","first-page":"363","DOI":"10.1016\/0168-9274(85)90001-7","volume":"1","author":"K. Burrage","year":"1985","unstructured":"K. Burrage, Order and stability of explicit multivalue methods, Appl. Numer. Math. 1 (1985) 363\u2013379.","journal-title":"Appl. Numer. Math."},{"key":"325258_CR3","doi-asserted-by":"crossref","first-page":"43","DOI":"10.1093\/imanum\/8.1.43","volume":"8","author":"K. Burrage","year":"1988","unstructured":"K. Burrage, Order properties of multivalue methods, IMA J. Numer. Anal. 8 (1988) 43\u201369.","journal-title":"IMA J. Numer. Anal."},{"key":"325258_CR4","doi-asserted-by":"crossref","first-page":"125","DOI":"10.1016\/0168-9274(93)90044-R","volume":"11","author":"K. Burrage","year":"1993","unstructured":"K. Burrage, The search for the holy grail, or: predictor-corrector methods for solving ODEIVPs, Appl. Numer. Math. 11 (1993) 125\u2013141.","journal-title":"Appl. Numer. Math."},{"key":"325258_CR5","doi-asserted-by":"crossref","DOI":"10.1093\/oso\/9780198534327.001.0001","volume-title":"Parallel and Sequential Methods for Ordinary Differential Equations","author":"K. Burrage","year":"1995","unstructured":"K. Burrage, Parallel and Sequential Methods for Ordinary Differential Equations (Oxford University Press, New York, 1995)."},{"key":"325258_CR6","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1090\/S0025-5718-1966-0189251-X","volume":"20","author":"J. C. Butcher","year":"1966","unstructured":"J. C. Butcher, On the convergence of numerical solutions to ordinary differential equations, Math. Comp. 20 (1966) 1\u201310.","journal-title":"Math. Comp."},{"key":"325258_CR7","doi-asserted-by":"crossref","first-page":"793","DOI":"10.1090\/S0025-5718-1973-0343620-7","volume":"27","author":"J. C. Butcher","year":"1973","unstructured":"J. C. Butcher, The order of numerical methods for ordinary differential equations, Math. Comp. 27 (1973) 793\u2013806.","journal-title":"Math. Comp."},{"key":"325258_CR8","unstructured":"Nguyen huu Cong and T. Mitsui, A class of explicit parallel two-step Runge-Kutta methods, in preparation."},{"key":"325258_CR9","doi-asserted-by":"crossref","first-page":"117","DOI":"10.1016\/0377-0427(94)90094-9","volume":"51","author":"N. h. Cong","year":"1994","unstructured":"Nguyen huu Cong, Parallel iteration of symmetric Runge-Kutta methods for non stiff initial value problems, J. Comput. Appl. Math. 51 (1994) 117\u2013125.","journal-title":"J. Comput. Appl. Math."},{"key":"325258_CR10","unstructured":"Nguyen huu Cong, Explicit parallel two-step Runge-Kutta-Nystr\u00f6m methods, Comput. Math. Appl., to appear."},{"key":"325258_CR11","doi-asserted-by":"crossref","first-page":"643","DOI":"10.1137\/0715043","volume":"15","author":"G. J. Cooper","year":"1978","unstructured":"G. J. Cooper, The order of convergence of general linear methods for ordinary differential equations, SIAM J. Numer. Anal. 15 (1978) 643\u2013661.","journal-title":"SIAM J. Numer. Anal."},{"key":"325258_CR12","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1145\/23002.27645","volume":"13","author":"W. H. Enright","year":"1987","unstructured":"W. H. Enright and J. D. Pryce, Two Fortran packages for assessing initial value methods, ACM Trans. Math. Software 13 (1987) 1\u201327.","journal-title":"ACM Trans. Math. Software"},{"key":"325258_CR13","first-page":"17","volume":"R-3","author":"A. Guillou","year":"1969","unstructured":"A. Guillou and J. L. Soul\u00e9, La r\u00e9solution num\u00e9rique des probl\u00e8mes diff\u00e9rentiels aux conditions initiales par des m\u00e9thodes de collocation, R.I.R.O. R-3 (1969) 17\u201344.","journal-title":"R.I.R.O."},{"key":"325258_CR14","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/BF02268387","volume":"13","author":"E. Hairer","year":"1974","unstructured":"E. Hairer and G. Wanner, On the Butcher group and general multivalue methods, Computing 13 (1974) 1\u201315.","journal-title":"Computing"},{"key":"325258_CR15","series-title":"Springer Series in Computational Mathematics","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-662-12607-3","volume-title":"Solving Ordinary Differential Equations I: Nonstiff Problems","author":"E. Hairer","year":"1987","unstructured":"E. Hairer and G. Wanner, Solving Ordinary Differential Equations I: Nonstiff Problems, Springer Series in Computational Mathematics (Springer, Berlin, 1987)."},{"key":"325258_CR16","series-title":"Springer Series in Computational Mathematics","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-662-09947-6","volume-title":"Solving Ordinary Differential Equations II: Stiff and Differential-Algebraic Problems","author":"E. Hairer","year":"1991","unstructured":"E. Hairer, S. P. N\u00f8rsett and G. Wanner, Solving Ordinary Differential Equations II: Stiff and Differential-Algebraic Problems, Springer Series in Computational Mathematics (Springer, Berlin, 1991)."},{"key":"325258_CR17","volume-title":"Variable step integration of high order Runge-Kutta methods on parallel computers","author":"P. J. van der Houwen","year":"1988","unstructured":"P. J. van der Houwen and B. P. Sommeijer, Variable step integration of high order Runge-Kutta methods on parallel computers, Report NM-R8817, CWI, Amsterdam, The Netherlands (1988)."},{"key":"325258_CR18","doi-asserted-by":"crossref","first-page":"111","DOI":"10.1016\/0377-0427(90)90200-J","volume":"29","author":"P. J. van der Houwen","year":"1990","unstructured":"P. J. van der Houwen and B. P. Sommeijer, Parallel iteration of high-order Runge-Kutta methods with stepsize control, J. Comput. Appl. Math. 29 (1990) 111\u2013127.","journal-title":"J. Comput. Appl. Math."},{"key":"325258_CR19","doi-asserted-by":"crossref","first-page":"109","DOI":"10.1016\/0168-9274(93)90135-E","volume":"13","author":"P. J. van der Houwen","year":"1993","unstructured":"P. J. van der Houwen and Nguyen huu Cong, Parallel block predictor-corrector methods of Runge-Kutta type, Appl. Numer. Math. 13 (1993) 109\u2013123.","journal-title":"Appl. Numer. Math."},{"key":"325258_CR20","doi-asserted-by":"crossref","first-page":"603","DOI":"10.1137\/0709052","volume":"9","author":"T. E. Hull","year":"1972","unstructured":"T. E. Hull, W. E. Enright, B. M. Fellen and A. E. Sedgwick, Comparing numerical methods for ordinary differential equations, SIAM J. Numer. Anal. 9 (1972) 603\u2013637.","journal-title":"SIAM J. Numer. Anal."},{"key":"325258_CR21","doi-asserted-by":"crossref","first-page":"463","DOI":"10.1093\/imanum\/10.4.463","volume":"10","author":"A. Iserles","year":"1990","unstructured":"A. Iserles and S. P. N\u00f8rsett, On the theory of parallel Runge-Kutta methods, IMA J. Numer. Anal. 10 (1990) 463\u2013488.","journal-title":"IMA J. Numer. Anal."},{"key":"325258_CR22","first-page":"1","volume":"1","author":"Z. Jackiewicz","year":"1988","unstructured":"Z. Jackiewicz and S. Tracogna, A general class of two-step Runge-Kutta methods for ordinary differential equations, SIAM J. Numer. Anal. 1 (1988) 1\u201338.","journal-title":"SIAM J. Numer. Anal."},{"key":"325258_CR23","doi-asserted-by":"crossref","first-page":"49","DOI":"10.1137\/0732002","volume":"32","author":"K. R. Jackson","year":"1995","unstructured":"K. R. Jackson and S. P. N\u00f8rsett, The potential for parallelism in Runge-Kutta methods. Part I: RK formula in standard forms, SIAM J. Numer. Anal. 32 (1995) 49\u201382.","journal-title":"SIAM J. Numer. Anal."},{"key":"325258_CR24","volume-title":"Priblizhennoe Vyschisslenie Integralov","author":"V. I. Krylov","year":"1959","unstructured":"V. I. Krylov, Priblizhennoe Vyschisslenie Integralov (Gos. Izd. Fiz.-Mat. Lit., Moscow, 1959). English translation: Approximate Calculation of Integrals (Macmillan, New York, 1962)."},{"key":"325258_CR25","volume-title":"Some aspects of parallel Runge-Kutta methods","author":"I. Lie","year":"1987","unstructured":"I. Lie, Some aspects of parallel Runge-Kutta methods, Report No. 3\/87, University of Trondheim, Division Numerical Mathematics, Norway (1987)."},{"key":"325258_CR26","doi-asserted-by":"crossref","first-page":"65","DOI":"10.1090\/S0025-5718-1989-0971403-5","volume":"52","author":"I. Lie","year":"1989","unstructured":"I. Lie and S. P. N\u00f8rsett, Superconvergence for multistep collocation, Math. Comp. 52 (1989) 65\u201379.","journal-title":"Math. Comp."},{"key":"325258_CR27","series-title":"Lecture Notes in Mathematics","doi-asserted-by":"crossref","first-page":"103","DOI":"10.1007\/BFb0089234","volume-title":"Workshop on Numerical Methods for Ordinary Differential Equations, L'Aquila","author":"S. P. N\u00f8rsett","year":"1989","unstructured":"S. P. N\u00f8rsett and H. H. Simonsen, Aspects of parallel Runge-Kutta methods, in: Workshop on Numerical Methods for Ordinary Differential Equations, L'Aquila, ed. A. Bellen, Lecture Notes in Mathematics 1386 (Springer, Berlin, 1989) 103\u2013117."},{"key":"325258_CR28","doi-asserted-by":"crossref","first-page":"332","DOI":"10.1007\/BF01989754","volume":"33","author":"S. Schneider","year":"1993","unstructured":"S. Schneider, Numerical experiments with a multistep Radau method, BIT 33 (1993) 332\u2013350.","journal-title":"BIT"}],"container-title":["Advances in Computational Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1023\/A:1018930415863.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1023\/A:1018930415863\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1023\/A:1018930415863.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,5,16]],"date-time":"2025-05-16T23:24:43Z","timestamp":1747437883000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1023\/A:1018930415863"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1997,3]]},"references-count":28,"journal-issue":{"issue":"1-2","published-print":{"date-parts":[[1997,3]]}},"alternative-id":["325258"],"URL":"https:\/\/doi.org\/10.1023\/a:1018930415863","relation":{},"ISSN":["1019-7168","1572-9044"],"issn-type":[{"type":"print","value":"1019-7168"},{"type":"electronic","value":"1572-9044"}],"subject":[],"published":{"date-parts":[[1997,3]]}}}