{"id":"https://openalex.org/W2109866862","doi":"https://doi.org/10.1080/00207160701458716","title":"On the local and global errors of splitting approximations of reaction\u2013diffusion equations with high spatial gradients","display_name":"On the local and global errors of splitting approximations of reaction\u2013diffusion equations with high spatial gradients","publication_year":2007,"publication_date":"2007-06-01","ids":{"openalex":"https://openalex.org/W2109866862","doi":"https://doi.org/10.1080/00207160701458716","mag":"2109866862"},"language":"en","primary_location":{"id":"doi:10.1080/00207160701458716","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207160701458716","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"],"host_organization_lineage_names":["Taylor & Francis"],"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/A5112296910","display_name":"St\u00e9phane Descombes","orcid":null},"institutions":[{"id":"https://openalex.org/I113428412","display_name":"\u00c9cole Normale Sup\u00e9rieure de Lyon","ror":"https://ror.org/04zmssz18","country_code":"FR","type":"education","lineage":["https://openalex.org/I113428412","https://openalex.org/I203339264"]},{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I4210160577","display_name":"Unit\u00e9 de Math\u00e9matiques Pures et Appliqu\u00e9es","ror":"https://ror.org/05n21n105","country_code":"FR","type":"facility","lineage":["https://openalex.org/I113428412","https://openalex.org/I1294671590","https://openalex.org/I203339264","https://openalex.org/I4210160577"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"St\u00e9phane Descombes","raw_affiliation_strings":["Unit\u00e9 de Math\u00e9matiques Pures et Appliqu\u00e9es , CNRS UMR 5669, Ecole Normale Sup\u00e9rieure de Lyon, 46 All\u00e9e d\u2019Italie, 69364 Lyon Cedex, 07, France","Unit\u00e9 de Math\u00e9matiques Pures et Appliqu\u00e9es, France#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Unit\u00e9 de Math\u00e9matiques Pures et Appliqu\u00e9es , CNRS UMR 5669, Ecole Normale Sup\u00e9rieure de Lyon, 46 All\u00e9e d\u2019Italie, 69364 Lyon Cedex, 07, France","institution_ids":["https://openalex.org/I113428412","https://openalex.org/I4210160577","https://openalex.org/I1294671590"]},{"raw_affiliation_string":"Unit\u00e9 de Math\u00e9matiques Pures et Appliqu\u00e9es, France#TAB#","institution_ids":["https://openalex.org/I4210160577"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5105817382","display_name":"Thierry Dumont","orcid":null},"institutions":[{"id":"https://openalex.org/I4210104796","display_name":"Institut Camille Jordan","ror":"https://ror.org/01ekw7f87","country_code":"FR","type":"facility","lineage":["https://openalex.org/I100532134","https://openalex.org/I112936343","https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I203339264","https://openalex.org/I203339264","https://openalex.org/I203339264","https://openalex.org/I203339264","https://openalex.org/I4210104796","https://openalex.org/I4405259976","https://openalex.org/I48430043"]},{"id":"https://openalex.org/I100532134","display_name":"Universit\u00e9 Claude Bernard Lyon 1","ror":"https://ror.org/029brtt94","country_code":"FR","type":"education","lineage":["https://openalex.org/I100532134","https://openalex.org/I203339264"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Thierry Dumont","raw_affiliation_strings":["Institut Camille Jordan, Universit\u00e9 Claude Bernard Lyon 1 , 43 Boulevard du 11 Novembre 1918, 69622 Villeurbanne Cedex, France","Institut Camille Jordan, Universit\u00e9 Claude Bernard - Lyon 1, France#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institut Camille Jordan, Universit\u00e9 Claude Bernard Lyon 1 , 43 Boulevard du 11 Novembre 1918, 69622 Villeurbanne Cedex, France","institution_ids":["https://openalex.org/I4210104796","https://openalex.org/I100532134"]},{"raw_affiliation_string":"Institut Camille Jordan, Universit\u00e9 Claude Bernard - Lyon 1, France#TAB#","institution_ids":["https://openalex.org/I4210104796","https://openalex.org/I100532134"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5008121410","display_name":"Violaine Louvet","orcid":"https://orcid.org/0000-0002-8742-8952"},"institutions":[{"id":"https://openalex.org/I4210104796","display_name":"Institut Camille Jordan","ror":"https://ror.org/01ekw7f87","country_code":"FR","type":"facility","lineage":["https://openalex.org/I100532134","https://openalex.org/I112936343","https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I203339264","https://openalex.org/I203339264","https://openalex.org/I203339264","https://openalex.org/I203339264","https://openalex.org/I4210104796","https://openalex.org/I4405259976","https://openalex.org/I48430043"]},{"id":"https://openalex.org/I100532134","display_name":"Universit\u00e9 Claude Bernard Lyon 1","ror":"https://ror.org/029brtt94","country_code":"FR","type":"education","lineage":["https://openalex.org/I100532134","https://openalex.org/I203339264"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Violaine Louvet","raw_affiliation_strings":["Institut Camille Jordan, Universit\u00e9 Claude Bernard Lyon 1 , 43 Boulevard du 11 Novembre 1918, 69622 Villeurbanne Cedex, France","Institut Camille Jordan, Universit\u00e9 Claude Bernard - Lyon 1, France#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institut Camille Jordan, Universit\u00e9 Claude Bernard Lyon 1 , 43 Boulevard du 11 Novembre 1918, 69622 Villeurbanne Cedex, France","institution_ids":["https://openalex.org/I4210104796","https://openalex.org/I100532134"]},{"raw_affiliation_string":"Institut Camille Jordan, Universit\u00e9 Claude Bernard - Lyon 1, France#TAB#","institution_ids":["https://openalex.org/I4210104796","https://openalex.org/I100532134"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5055196143","display_name":"Marc Massot","orcid":"https://orcid.org/0000-0001-8823-7667"},"institutions":[{"id":"https://openalex.org/I4210127286","display_name":"Laboratoire d'\u00c9nerg\u00e9tique Mol\u00e9culaire et Macroscopique, Combustion","ror":"https://ror.org/02wy3s959","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I277688954","https://openalex.org/I4210095849","https://openalex.org/I4210107720","https://openalex.org/I4210127286"]},{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I216852786","display_name":"\u00c9cole Centrale Paris","ror":"https://ror.org/00v0y5771","country_code":"FR","type":"education","lineage":["https://openalex.org/I216852786"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Marc Massot","raw_affiliation_strings":["Laboratoire EM2C , UPR CNRS 288, Ecole Centrale Paris, Grande Voie des Vignes, 92295 Chatenay-Malabry Cedex, France","Laboratoire EM2C, France#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Laboratoire EM2C , UPR CNRS 288, Ecole Centrale Paris, Grande Voie des Vignes, 92295 Chatenay-Malabry Cedex, France","institution_ids":["https://openalex.org/I216852786","https://openalex.org/I4210127286","https://openalex.org/I1294671590"]},{"raw_affiliation_string":"Laboratoire EM2C, France#TAB#","institution_ids":["https://openalex.org/I4210127286"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5112296910"],"corresponding_institution_ids":["https://openalex.org/I113428412","https://openalex.org/I1294671590","https://openalex.org/I4210160577"],"apc_list":null,"apc_paid":null,"fwci":1.016,"has_fulltext":false,"cited_by_count":13,"citation_normalized_percentile":{"value":0.78167368,"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":"749","last_page":"765"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12727","display_name":"Differential Equations and Numerical Methods","score":0.9995999932289124,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9991999864578247,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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":0.8653459548950195},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.8428812026977539},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.553659200668335},{"id":"https://openalex.org/keywords/commutator","display_name":"Commutator","score":0.5246439576148987},{"id":"https://openalex.org/keywords/ordinary-differential-equation","display_name":"Ordinary differential equation","score":0.5216475129127502},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.48510825634002686},{"id":"https://openalex.org/keywords/derivative","display_name":"Derivative (finance)","score":0.46146705746650696},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.43389222025871277},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.40895408391952515},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3839006721973419},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.15210700035095215},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.08386287093162537}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8653459548950195},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.8428812026977539},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.553659200668335},{"id":"https://openalex.org/C145620117","wikidata":"https://www.wikidata.org/wiki/Q2989763","display_name":"Commutator","level":4,"score":0.5246439576148987},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.5216475129127502},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.48510825634002686},{"id":"https://openalex.org/C111771559","wikidata":"https://www.wikidata.org/wiki/Q66295","display_name":"Derivative (finance)","level":2,"score":0.46146705746650696},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.43389222025871277},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.40895408391952515},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3839006721973419},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.15210700035095215},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.08386287093162537},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"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/C73648015","wikidata":"https://www.wikidata.org/wiki/Q6543817","display_name":"Lie conformal algebra","level":3,"score":0.0},{"id":"https://openalex.org/C106159729","wikidata":"https://www.wikidata.org/wiki/Q2294553","display_name":"Financial economics","level":1,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1080/00207160701458716","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207160701458716","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"],"host_organization_lineage_names":["Taylor & Francis"],"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"},{"id":"pmh:oai:HAL:hal-00175003v1","is_oa":false,"landing_page_url":"https://hal.science/hal-00175003","pdf_url":null,"source":{"id":"https://openalex.org/S4406922466","display_name":"SPIRE - Sciences Po Institutional REpository","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"International Journal of Computer Mathematics, 2007, 84 (6), pp.749 - 765. &#x27E8;10.1080/00207160701458716&#x27E9;","raw_type":"Journal articles"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":13,"referenced_works":["https://openalex.org/W1544770838","https://openalex.org/W1583602735","https://openalex.org/W1592378316","https://openalex.org/W1974477559","https://openalex.org/W2016529055","https://openalex.org/W2031981727","https://openalex.org/W2044077544","https://openalex.org/W2049161806","https://openalex.org/W2078824148","https://openalex.org/W2119181847","https://openalex.org/W2947056241","https://openalex.org/W2969232873","https://openalex.org/W4254432473"],"related_works":["https://openalex.org/W2006251942","https://openalex.org/W4302027589","https://openalex.org/W2364741597","https://openalex.org/W1492103595","https://openalex.org/W2728978206","https://openalex.org/W1864774435","https://openalex.org/W946352265","https://openalex.org/W2365603414","https://openalex.org/W2999616507","https://openalex.org/W2748563398"],"abstract_inverted_index":{"In":[0],"this":[1],"paper":[2],"we":[3,29,66],"study":[4,67],"the":[5,11,35,49,68,86,90,98],"approximation":[6],"by":[7],"splitting":[8],"techniques":[9],"of":[10,51,70,94],"ordinary":[12],"differential":[13,73],"equation":[14],"U\u02d9+A":[15],"U+B":[16],"U=0,":[17],"U(0)=U":[18],"0":[19,43,96],"with":[20,54],"A":[21,38,101],"and":[22,41,84,97,102],"B":[23],"two":[24,81],"matrices.":[25],"We":[26,75],"assume":[27],"that":[28,37],"have":[30],"a":[31,45,52,55,71],"stiff":[32,87],"problem":[33],"in":[34,85],"sense":[36],"is":[39,44,48],"ill-conditionned":[40],"U":[42,95],"vector":[46],"which":[47],"discretization":[50,69],"function":[53],"very":[56],"high":[57],"derivative.":[58],"This":[59],"situation":[60],"may":[61],"appear":[62],"for":[63,80],"example":[64],"when":[65],"partial":[72],"equation.":[74],"prove":[76],"some":[77],"error":[78],"estimates":[79,91],"general":[82],"matrices":[83],"case,":[88],"where":[89],"are":[92],"independent":[93],"commutator":[99],"between":[100],"B.":[103]},"counts_by_year":[{"year":2020,"cited_by_count":1},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":1}],"updated_date":"2026-04-25T08:17:42.794288","created_date":"2025-10-10T00:00:00"}
