{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,30]],"date-time":"2026-04-30T00:21:08Z","timestamp":1777508468538,"version":"3.51.4"},"reference-count":31,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2020,7,23]],"date-time":"2020-07-23T00:00:00Z","timestamp":1595462400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2020,7,23]],"date-time":"2020-07-23T00:00:00Z","timestamp":1595462400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/501100000038","name":"NSERC","doi-asserted-by":"crossref","id":[{"id":"10.13039\/501100000038","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Comp. Appl. Math."],"published-print":{"date-parts":[[2020,9]]},"DOI":"10.1007\/s40314-020-01254-z","type":"journal-article","created":{"date-parts":[[2020,7,23]],"date-time":"2020-07-23T21:21:09Z","timestamp":1595539269000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Analysis of time-stepping methods for the monodomain model"],"prefix":"10.1007","volume":"39","author":[{"given":"Thomas","family":"Roy","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yves","family":"Bourgault","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Charles","family":"Pierre","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2020,7,23]]},"reference":[{"issue":"3","key":"1254_CR1","doi-asserted-by":"crossref","first-page":"797","DOI":"10.1137\/0732037","volume":"32","author":"UM Ascher","year":"1995","unstructured":"Ascher UM, Ruuth SJ, Wetton BTR (1995) Implicit-explicit methods for time-dependent partial differential equations. SIAM J Numer Anal 32(3):797\u2013823","journal-title":"SIAM J Numer Anal"},{"key":"1254_CR2","doi-asserted-by":"crossref","first-page":"177","DOI":"10.1113\/jphysiol.1977.sp011853","volume":"268","author":"GW Beeler","year":"1977","unstructured":"Beeler GW, Reuter H (1977) Reconstruction of the action potential of ventricular myocardial fibres. J Physiol 268:177\u2013210","journal-title":"J Physiol"},{"issue":"4","key":"1254_CR3","first-page":"542","volume":"58","author":"JW Cain","year":"2011","unstructured":"Cain JW (2011) Taking math to heart: mathematical challenges in cardiac electrophysiology. Not AMS 58(4):542\u2013549","journal-title":"Not AMS"},{"issue":"1","key":"1254_CR4","doi-asserted-by":"crossref","first-page":"22","DOI":"10.1016\/j.pbiomolbio.2010.05.008","volume":"104","author":"R Clayton","year":"2011","unstructured":"Clayton R, Bernus O, Cherry E, Dierckx H, Fenton F, Mirabella L, Panfilov A, Sachse F, Seemann G, Zhang H (2011) Models of cardiac tissue electrophysiology: progress, challenges and open questions. Prog Biophys Mol Biol 104(1):22\u201348","journal-title":"Prog Biophys Mol Biol"},{"issue":"5","key":"1254_CR5","doi-asserted-by":"crossref","first-page":"2443","DOI":"10.1137\/070680503","volume":"46","author":"M Ethier","year":"2008","unstructured":"Ethier M, Bourgault Y (2008) Semi-implicit time-discretization schemes for the bidomain model. SIAM J Numer Anal 46(5):2443\u20132468","journal-title":"SIAM J Numer Anal"},{"issue":"6","key":"1254_CR6","doi-asserted-by":"crossref","first-page":"A2656","DOI":"10.1137\/140975231","volume":"37","author":"JL Guermond","year":"2015","unstructured":"Guermond JL, Minev P (2015) High-order time stepping for the incompressible Navier\u2013Stokes equations. SIAM J Sci Comput 37(6):A2656\u2013A2681","journal-title":"SIAM J Sci Comput"},{"key":"1254_CR7","unstructured":"Hairer E, N\u00f8rsett S, Wanner G (1993) Solving ordinary differential equations I: Nonstiff Problems. Springer Series in Comp. Math., vol.\u00a08. Springer, New York"},{"key":"1254_CR8","doi-asserted-by":"crossref","unstructured":"Hairer E, Wanner G (1996) Solving ordinary differential equations II: stiff problems and differential-algebraic problems. Springer Series in Comp. Math., vol.\u00a014. Springer, New York","DOI":"10.1007\/978-3-642-05221-7"},{"issue":"3","key":"1254_CR9","first-page":"427","volume":"8","author":"M Hanslien","year":"2011","unstructured":"Hanslien M, Artebrant R, Tveito A, Lines GT, Cai X (2011) Stability of two time-integrators for the Aliev\u2013Panfilov system. Int J Numer Anal Model 8(3):427\u2013442","journal-title":"Int J Numer Anal Model"},{"key":"1254_CR10","doi-asserted-by":"crossref","first-page":"500","DOI":"10.1113\/jphysiol.1952.sp004764","volume":"117","author":"A Hodgkin","year":"1952","unstructured":"Hodgkin A, Huxley A (1952) A quantitative description of membrane current and its applications to conduction and excitation in nerves. J Physiol 117:500\u2013544","journal-title":"J Physiol"},{"issue":"1","key":"1254_CR11","first-page":"234","volume":"8","author":"J Keener","year":"1998","unstructured":"Keener J, Bogar K (1998) A numerical method for the solution of the bidomain equations in cardiac tissue. Chaos: An Interdisciplinary. J Nonlinear Sci 8(1):234\u2013241","journal-title":"J Nonlinear Sci"},{"key":"1254_CR12","volume-title":"Mathematical Physiology","author":"J Keener","year":"2004","unstructured":"Keener J, Sneyd J (2004) Mathematical Physiology. Springer, New York"},{"issue":"1\u20134","key":"1254_CR13","doi-asserted-by":"crossref","first-page":"241","DOI":"10.1023\/A:1015113017248","volume":"17","author":"W Kress","year":"2002","unstructured":"Kress W, Gustafsson B (2002) Deferred correction methods for initial boundary value problems. J Sci Comput 17(1\u20134):241\u2013251","journal-title":"J Sci Comput"},{"issue":"9","key":"1254_CR14","doi-asserted-by":"crossref","first-page":"2506","DOI":"10.1109\/TBME.2012.2205575","volume":"59","author":"M Marsh","year":"2012","unstructured":"Marsh M, Torabi S, Spiteri R (2012) The secrets to the success of the Rush\u2013Larsen method and its generalizations. IEEE Trans Biomed Eng 59(9):2506\u20132515","journal-title":"IEEE Trans Biomed Eng"},{"key":"1254_CR15","doi-asserted-by":"crossref","first-page":"767","DOI":"10.1016\/S0092-8240(03)00041-7","volume":"65","author":"C Mitchell","year":"2003","unstructured":"Mitchell C, Schaeffer D (2003) A two-current model for the dynamics of cardiac membrane. Bull Math Biol 65:767\u2013793","journal-title":"Bull Math Biol"},{"key":"1254_CR16","first-page":"234","volume":"35","author":"M Perego","year":"2009","unstructured":"Perego M, Veneziani A (2009) An efficient generalization of the Rush\u2013Larsen method for solving electro-physiology membrane equations. Electron Trans Numer Anal 35:234\u2013256","journal-title":"Electron Trans Numer Anal"},{"issue":"5","key":"1254_CR17","doi-asserted-by":"crossref","first-page":"951","DOI":"10.1109\/TBME.2006.889204","volume":"54","author":"S Puwal","year":"2007","unstructured":"Puwal S, Roth B (2007) Forward Euler stability of the bidomain model of cardiac tissue. IEEE Trans Biomed Eng 54(5):951","journal-title":"IEEE Trans Biomed Eng"},{"key":"1254_CR18","unstructured":"Report 84F0209X, Statistics Canada (2009) Mortality, summary list of causes. https:\/\/www150.statcan.gc.ca\/n1\/en\/catalogue\/84F0209X"},{"key":"1254_CR19","unstructured":"Roy T (2015) Time-stepping methods in cardiac electrophysiology. Master\u2019s thesis, University of Ottawa, Canada"},{"issue":"4","key":"1254_CR20","doi-asserted-by":"crossref","first-page":"389","DOI":"10.1109\/TBME.1978.326270","volume":"25","author":"S Rush","year":"1978","unstructured":"Rush S, Larsen H (1978) A practical algorithm for solving dynamic membrane equations. IEEE Trans Biomed Eng 25(4):389\u2013392","journal-title":"IEEE Trans Biomed Eng"},{"issue":"6","key":"1254_CR21","doi-asserted-by":"crossref","first-page":"871","DOI":"10.1080\/00207160701458724","volume":"84","author":"H Schroll","year":"2007","unstructured":"Schroll H, Lines G, Tveito A (2007) On the accuracy of operator splitting for the monodomain model of electrophysiology. Int J Comput Math 84(6):871\u2013885","journal-title":"Int J Comput Math"},{"issue":"5","key":"1254_CR22","doi-asserted-by":"crossref","first-page":"1488","DOI":"10.1109\/TBME.2007.914677","volume":"55","author":"R Spiteri","year":"2008","unstructured":"Spiteri R, Dean R (2008) On the performance of an implicit-explicit Runge\u2013Kutta method in models of cardiac electrical activity. IEEE Trans Biomed Eng 55(5):1488\u20131495","journal-title":"IEEE Trans Biomed Eng"},{"key":"1254_CR23","doi-asserted-by":"crossref","first-page":"3592","DOI":"10.1007\/s10439-010-0100-9","volume":"38","author":"R Spiteri","year":"2010","unstructured":"Spiteri R, Dean R (2010) Stiffness analysis of cardiac electrophysiological models. Ann Biomed Eng 38:3592\u20133604","journal-title":"Ann Biomed Eng"},{"key":"1254_CR24","doi-asserted-by":"crossref","first-page":"506","DOI":"10.1137\/0705041","volume":"5","author":"G Strang","year":"1968","unstructured":"Strang G (1968) On the construction and comparison of difference schemes. SIAM J Numer Anal 5:506\u2013517","journal-title":"SIAM J Numer Anal"},{"issue":"10","key":"1254_CR25","doi-asserted-by":"crossref","first-page":"2546","DOI":"10.1109\/TBME.2009.2014739","volume":"56","author":"J Sundnes","year":"2009","unstructured":"Sundnes J, Artebrant R, Skavhaug O, Tveito A (2009) A second-order algorithm for solving dynamic cell membrane equations. IEEE Trans Biomed Eng 56(10):2546\u20132548","journal-title":"IEEE Trans Biomed Eng"},{"key":"1254_CR26","unstructured":"Sundnes J, Lines G, Cai, X, BN, Mardal KA, Tveito A (2006) Computing the electrical activity in the heart. Springer-Verlag, Berlin Heidelberg"},{"key":"1254_CR27","unstructured":"The finite element code CHORAL (2020). http:\/\/cpierre1.perso.univ-pau.fr\/ or alternatively at https:\/\/plmlab.math.cnrs.fr\/cpierre1\/choral"},{"key":"1254_CR28","first-page":"40","volume":"2","author":"ZS Torabi","year":"2014","unstructured":"Torabi ZS, Marsh M, Sundnes J, Spiteri R (2014) Stable time integration suppresses unphysical oscillations in the bidomain model. Comput Phys 2:40","journal-title":"Comput Phys"},{"issue":"2","key":"1254_CR29","doi-asserted-by":"crossref","first-page":"645","DOI":"10.1016\/j.jcp.2003.11.014","volume":"196","author":"J Trangenstein","year":"2004","unstructured":"Trangenstein J, Kim C (2004) Operator splitting and adaptive mesh refinement for the Luo\u2013Rudy I model. J Comput Phys 196(2):645\u2013679","journal-title":"J Comput Phys"},{"key":"1254_CR30","doi-asserted-by":"crossref","first-page":"H1573","DOI":"10.1152\/ajpheart.00794.2003","volume":"286","author":"K ten Tusscher","year":"2004","unstructured":"ten Tusscher K, Noble D, Noble P, Panfilov A (2004) A model for human ventricular tissue. Am J Physiol Heart Circ Physiol 286:H1573\u2013H1589","journal-title":"Am J Physiol Heart Circ Physiol"},{"key":"1254_CR31","doi-asserted-by":"crossref","first-page":"119","DOI":"10.1146\/annurev.bioeng.2.1.119","volume":"2","author":"R Winslow","year":"2000","unstructured":"Winslow R, Scollan D, Holmes A, Yung C, Zhang J, Jafri M (2000) Electrophysiological modeling of cardiac ventricular function: from cell to organ. Annu Rev Biomed Eng 2:119","journal-title":"Annu Rev Biomed Eng"}],"container-title":["Computational and Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s40314-020-01254-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s40314-020-01254-z\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s40314-020-01254-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,7,22]],"date-time":"2021-07-22T23:27:55Z","timestamp":1626996475000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s40314-020-01254-z"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,7,23]]},"references-count":31,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2020,9]]}},"alternative-id":["1254"],"URL":"https:\/\/doi.org\/10.1007\/s40314-020-01254-z","relation":{},"ISSN":["2238-3603","1807-0302"],"issn-type":[{"value":"2238-3603","type":"print"},{"value":"1807-0302","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,7,23]]},"assertion":[{"value":"8 November 2017","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"17 May 2020","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"7 July 2020","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"23 July 2020","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}],"article-number":"230"}}