{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,4]],"date-time":"2026-05-04T13:43:31Z","timestamp":1777902211123,"version":"3.51.4"},"reference-count":25,"publisher":"SAGE Publications","issue":"4","license":[{"start":{"date-parts":[[2011,6,7]],"date-time":"2011-06-07T00:00:00Z","timestamp":1307404800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"content-domain":{"domain":["journals.sagepub.com"],"crossmark-restriction":true},"short-container-title":["SIMULATION"],"published-print":{"date-parts":[[2012,4]]},"abstract":"<jats:p>In this paper we introduce new classes of numerical ordinary differential equation (ODE) solvers that base their internal discretization method on state quantization instead of time slicing. These solvers have been coined quantized state system (QSS) simulators. The primary result of the research described in this article is a first-order accurate QSS-based stiff system solver, called the backward QSS (BQSS). The numerical properties of this new algorithm are discussed, and it is shown that this algorithm exhibits properties that make it a potentially attractive alternative to the classical numerical ODE solvers. Some simulation examples illustrate the advantages of this method. As a collateral result, a first-order accurate QSS-based solver designed for solving marginally stable systems is briefly outlined as well. This new method, called the centered QSS (CQSS), is successfully applied to a challenging benchmark problem describing a high-order system that is simultaneously stiff and marginally stable. However, the primary emphasis of this article is on the BQSS method, that is, on a stiff system solver based on state quantization.<\/jats:p>","DOI":"10.1177\/0037549711403645","type":"journal-article","created":{"date-parts":[[2011,6,7]],"date-time":"2011-06-07T23:56:26Z","timestamp":1307490986000},"page":"387-407","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":22,"title":["Quantization-based new integration methods for stiff ordinary differential equations"],"prefix":"10.1177","volume":"88","author":[{"given":"Gustavo","family":"Migoni","sequence":"first","affiliation":[{"name":"Laboratorio de Sistemas Din\u00e1micos, FCEIA\u2009-\u2009UNR\u2009-\u2009CIFASIS- CONICET, Argentina."}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ernesto","family":"Kofman","sequence":"additional","affiliation":[{"name":"Laboratorio de Sistemas Din\u00e1micos, FCEIA\u2009-\u2009UNR\u2009-\u2009CIFASIS- CONICET, Argentina."}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Fran\u00e7ois","family":"Cellier","sequence":"additional","affiliation":[{"name":"Department of Computer Science, ETH Zurich, Switzerland."}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"179","published-online":{"date-parts":[[2011,6,7]]},"reference":[{"key":"bibr1-0037549711403645","volume-title":"Theory of modeling and simulation","author":"Zeigler B","year":"2000","edition":"2"},{"key":"bibr2-0037549711403645","doi-asserted-by":"publisher","DOI":"10.1117\/12.319354"},{"key":"bibr3-0037549711403645","first-page":"123","volume":"18","author":"Kofman E","year":"2001","journal-title":"Trans SCS"},{"key":"bibr4-0037549711403645","doi-asserted-by":"publisher","DOI":"10.1177\/0037549702078002206"},{"key":"bibr5-0037549711403645","doi-asserted-by":"publisher","DOI":"10.1007\/s10543-006-0078-8"},{"key":"bibr6-0037549711403645","first-page":"60","volume-title":"Proceedings of the Numerical Analysis Conference","author":"Dahlquist G","year":"1975"},{"key":"bibr7-0037549711403645","doi-asserted-by":"publisher","DOI":"10.1145\/362566.362571"},{"key":"bibr8-0037549711403645","volume-title":"Continuous system simulation","author":"Cellier FE","year":"2006"},{"key":"bibr9-0037549711403645","doi-asserted-by":"publisher","DOI":"10.1137\/S1064827502418379"},{"key":"bibr10-0037549711403645","unstructured":"Nutaro J. Parallel discrete event simulation with application to continuous systems. PhD thesis, The University of Arizona, 2003."},{"key":"bibr11-0037549711403645","doi-asserted-by":"publisher","DOI":"10.1109\/CDC.2006.377483"},{"key":"bibr12-0037549711403645","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-09947-6"},{"key":"bibr13-0037549711403645","volume-title":"Geometric numerical integration structure-preserving algorithms for ordinary differential equations","author":"Hairer E","year":"2002"},{"key":"bibr14-0037549711403645","first-page":"101","volume":"36","author":"Kofman E","year":"2006","journal-title":"Lat Am Appl Res"},{"key":"bibr15-0037549711403645","doi-asserted-by":"publisher","DOI":"10.1109\/PADS.2007.9"},{"key":"bibr16-0037549711403645","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2007.08.015"},{"key":"bibr17-0037549711403645","unstructured":"Migoni G. Simulaci\u00f3n por Cuantificaci\u00f3n de Sistemas Stiff.\n                      PhD thesis\n                      , Facultad de Ciencias Exactas, Ingeniera y Agrimensura. Rosario, Argentina: Universidad Nacional de Rosario, Rosario, Argentina, 2010."},{"key":"bibr18-0037549711403645","volume-title":"Numerical methods for ordinary differential systems: The initial value problem","author":"Lambert JD","year":"1991"},{"key":"bibr19-0037549711403645","doi-asserted-by":"publisher","DOI":"10.1080\/13647830500352465"},{"key":"bibr20-0037549711403645","doi-asserted-by":"publisher","DOI":"10.1016\/j.automatica.2005.04.024"},{"key":"bibr21-0037549711403645","doi-asserted-by":"publisher","DOI":"10.1080\/00207170600611265"},{"key":"bibr22-0037549711403645","doi-asserted-by":"publisher","DOI":"10.1177\/0037549710368029"},{"key":"bibr23-0037549711403645","unstructured":"Jammalamadaka R. Activity characterization of spatial models: application to discrete event solution of partial differential equations. Master\u2019s thesis, The University of Arizona, 2003."},{"key":"bibr24-0037549711403645","doi-asserted-by":"publisher","DOI":"10.1145\/23002.27645"},{"key":"bibr25-0037549711403645","volume-title":"Nonlinear systems","author":"Khalil H","year":"1996","edition":"2"}],"container-title":["SIMULATION"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.1177\/0037549711403645","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.1177\/0037549711403645","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,5,1]],"date-time":"2026-05-01T11:23:06Z","timestamp":1777634586000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/10.1177\/0037549711403645"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011,6,7]]},"references-count":25,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2012,4]]}},"alternative-id":["10.1177\/0037549711403645"],"URL":"https:\/\/doi.org\/10.1177\/0037549711403645","relation":{},"ISSN":["0037-5497","1741-3133"],"issn-type":[{"value":"0037-5497","type":"print"},{"value":"1741-3133","type":"electronic"}],"subject":[],"published":{"date-parts":[[2011,6,7]]}}}