{"id":"https://openalex.org/W2092915009","doi":"https://doi.org/10.1080/00207160701458724","title":"On the accuracy of operator splitting for the monodomain model of electrophysiology","display_name":"On the accuracy of operator splitting for the monodomain model of electrophysiology","publication_year":2007,"publication_date":"2007-06-01","ids":{"openalex":"https://openalex.org/W2092915009","doi":"https://doi.org/10.1080/00207160701458724","mag":"2092915009"},"language":"en","primary_location":{"id":"doi:10.1080/00207160701458724","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207160701458724","pdf_url":null,"source":{"id":"https://openalex.org/S124867444","display_name":"International Journal of Computer Mathematics","issn_l":"0020-7160","issn":["0020-7160","1026-7425","1029-0265"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547","https://openalex.org/P4310320449"],"host_organization_lineage_names":["Taylor & Francis","Informa"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Computer Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5027317343","display_name":"Hans Joachim Schroll","orcid":"https://orcid.org/0000-0002-5301-2916"},"institutions":[{"id":"https://openalex.org/I187531555","display_name":"Lund University","ror":"https://ror.org/012a77v79","country_code":"SE","type":"education","lineage":["https://openalex.org/I187531555"]}],"countries":["SE"],"is_corresponding":true,"raw_author_name":"H. J. Schroll","raw_affiliation_strings":["Centre for Mathematical Sciences, Lund University, Box 118, SE\u2013221 00, Lund, Sweden","Centre for Mathematical Sciences, Lund University, LUND, Sweden"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Centre for Mathematical Sciences, Lund University, Box 118, SE\u2013221 00, Lund, Sweden","institution_ids":["https://openalex.org/I187531555"]},{"raw_affiliation_string":"Centre for Mathematical Sciences, Lund University, LUND, Sweden","institution_ids":["https://openalex.org/I187531555"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5013534678","display_name":"Glenn Terje Lines","orcid":"https://orcid.org/0000-0002-5512-8525"},"institutions":[{"id":"https://openalex.org/I2799829267","display_name":"Simula Research Laboratory","ror":"https://ror.org/00vn06n10","country_code":"NO","type":"facility","lineage":["https://openalex.org/I2799829267"]}],"countries":["NO"],"is_corresponding":false,"raw_author_name":"G. T. Lines","raw_affiliation_strings":["Simula Research Laboratory, Box 134, N\u20131325, Lysaker, Norway","Simula Research Laboratory Lysaker, Norway"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Simula Research Laboratory, Box 134, N\u20131325, Lysaker, Norway","institution_ids":["https://openalex.org/I2799829267"]},{"raw_affiliation_string":"Simula Research Laboratory Lysaker, Norway","institution_ids":["https://openalex.org/I2799829267"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5016700859","display_name":"Aslak Tveito","orcid":"https://orcid.org/0000-0003-2362-146X"},"institutions":[{"id":"https://openalex.org/I2799829267","display_name":"Simula Research Laboratory","ror":"https://ror.org/00vn06n10","country_code":"NO","type":"facility","lineage":["https://openalex.org/I2799829267"]}],"countries":["NO"],"is_corresponding":false,"raw_author_name":"A. Tveito","raw_affiliation_strings":["Simula Research Laboratory, Box 134, N\u20131325, Lysaker, Norway","Simula Research Laboratory Lysaker, Norway"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Simula Research Laboratory, Box 134, N\u20131325, Lysaker, Norway","institution_ids":["https://openalex.org/I2799829267"]},{"raw_affiliation_string":"Simula Research Laboratory Lysaker, Norway","institution_ids":["https://openalex.org/I2799829267"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5027317343"],"corresponding_institution_ids":["https://openalex.org/I187531555"],"apc_list":null,"apc_paid":null,"fwci":0.4634,"has_fulltext":false,"cited_by_count":19,"citation_normalized_percentile":{"value":0.68385925,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"84","issue":"6","first_page":"871","last_page":"885"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10323","display_name":"Analog and Mixed-Signal Circuit Design","score":0.9919000267982483,"subfield":{"id":"https://openalex.org/subfields/2204","display_name":"Biomedical Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10323","display_name":"Analog and Mixed-Signal Circuit Design","score":0.9919000267982483,"subfield":{"id":"https://openalex.org/subfields/2204","display_name":"Biomedical Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10382","display_name":"Quantum and electron transport phenomena","score":0.9901000261306763,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11187","display_name":"Nonlinear Dynamics and Pattern Formation","score":0.9861000180244446,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7624529600143433},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.6624971032142639},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.6467713713645935},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.518059253692627},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4633503556251526},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.45747092366218567},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.29658740758895874}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7624529600143433},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.6624971032142639},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.6467713713645935},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.518059253692627},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4633503556251526},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.45747092366218567},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.29658740758895874},{"id":"https://openalex.org/C86339819","wikidata":"https://www.wikidata.org/wiki/Q407384","display_name":"Transcription factor","level":3,"score":0.0},{"id":"https://openalex.org/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/00207160701458724","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207160701458724","pdf_url":null,"source":{"id":"https://openalex.org/S124867444","display_name":"International Journal of Computer Mathematics","issn_l":"0020-7160","issn":["0020-7160","1026-7425","1029-0265"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547","https://openalex.org/P4310320449"],"host_organization_lineage_names":["Taylor & Francis","Informa"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Computer Mathematics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":24,"referenced_works":["https://openalex.org/W328073187","https://openalex.org/W1537346681","https://openalex.org/W1969075053","https://openalex.org/W1970950340","https://openalex.org/W1971947347","https://openalex.org/W1979156898","https://openalex.org/W1984336411","https://openalex.org/W1985940938","https://openalex.org/W1986333812","https://openalex.org/W1993325724","https://openalex.org/W2049161806","https://openalex.org/W2067779435","https://openalex.org/W2076774226","https://openalex.org/W2112522502","https://openalex.org/W2112544861","https://openalex.org/W2123189474","https://openalex.org/W2127926880","https://openalex.org/W2149369230","https://openalex.org/W2161837229","https://openalex.org/W2612743911","https://openalex.org/W2981328134","https://openalex.org/W3197540325","https://openalex.org/W4213388037","https://openalex.org/W4301866048"],"related_works":["https://openalex.org/W2006251942","https://openalex.org/W2364741597","https://openalex.org/W1492103595","https://openalex.org/W1864774435","https://openalex.org/W946352265","https://openalex.org/W3020787026","https://openalex.org/W2334479858","https://openalex.org/W2799209613","https://openalex.org/W2085754006","https://openalex.org/W1774782920"],"abstract_inverted_index":{"Nonlinear":[0],"systems":[1],"of":[2,8,42,63,74,77,83,92,97,110,253],"time":[3],"dependent":[4],"partial":[5],"differential":[6],"equations":[7,79],"real":[9],"life":[10],"phenomena":[11],"tend":[12],"to":[13,17,23,38,71,88,141,155,182,193,257],"be":[14,68,139],"very":[15,69],"complicated":[16],"solve":[18,24],"numerically.":[19],"One":[20],"common":[21],"approach":[22,66],"such":[25,64,124],"problems":[26],"is":[27,87,154,201,242,255],"by":[28,49,178,223],"applying":[29,179,205],"operator":[30,98,136,180],"splitting":[31,137,181,229],"which":[32],"introduces":[33],"subproblems":[34],"that":[35,103,189,211],"are":[36,45],"easier":[37,256],"handle.":[39],"The":[40,81,146],"solutions":[41],"the":[43,51,56,61,75,78,84,95,111,121,133,151,160,163,172,194,199,206,224,228,236],"subsystems":[44],"usually":[46],"glued":[47],"together":[48],"either":[50],"Godunov":[52],"method":[53,58],"(first-order)":[54],"or":[55],"Strang":[57],"(second-order).":[59],"However,":[60],"accuracy":[62,96],"an":[65,246],"may":[67],"hard":[70],"analyse":[72],"because":[73],"complexity":[76],"involved.":[80],"purpose":[82],"present":[85,152],"paper":[86,153],"introduce":[89],"another":[90],"line":[91],"reasoning":[93],"concerning":[94],"splitting.":[99],"Let":[100],"us":[101],"assume":[102],"a":[104,157,250],"fully":[105,164],"coupled":[106,165],"and":[107,128,171,240],"implicit":[108,166],"discretization":[109],"complete":[112],"system":[113],"has":[114],"been":[115],"developed.":[116],"Under":[117],"appropriate":[118],"conditions":[119],"on":[120,159],"continuous":[122,134],"problem,":[123],"discretizations":[125],"provide":[126],"reasonable":[127],"convergent":[129],"approximations.":[130],"As":[131],"in":[132,150],"case,":[135],"can":[138],"utilized":[140],"obtain":[142,156],"tractable":[143],"algebraic":[144],"subsystems.":[145],"problem":[147],"we":[148,187],"address":[149],"bound":[158],"difference":[161],"between":[162],"discrete":[167,184],"solutions,":[168,173],"u":[169,174,190,197,212,217,231,239],"h,":[170,175,213,232],"s,":[176],"obtained":[177,244],"these":[183],"equations.":[185],"Suppose":[186],"know":[188],"h":[191,218],"converges":[192,215,234],"analytical":[195,237],"solution":[196,238],"as":[198],"grid":[200,220],"properly":[202],"refined":[203],"and,":[204],"results":[207],"from":[208,249],"this":[209],"paper,":[210],"s":[214,233],"toward":[216,235],"under":[219],"refinement.":[221],"Then,":[222],"triangle":[225],"inequality,":[226],"also":[227],"approximation":[230,247],"convergence":[241],"thus":[243],"for":[245],"that,":[248],"practical":[251],"point":[252],"view,":[254],"compute.":[258]},"counts_by_year":[{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":3},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":1}],"updated_date":"2026-08-15T07:11:24.734988","created_date":"2025-10-10T00:00:00"}
