{"id":"https://openalex.org/W1994100237","doi":"https://doi.org/10.1016/0005-1098(82)90026-7","title":"Convergence in the boundary layer for singularly perturbed equations","display_name":"Convergence in the boundary layer for singularly perturbed equations","publication_year":1982,"publication_date":"1982-01-01","ids":{"openalex":"https://openalex.org/W1994100237","doi":"https://doi.org/10.1016/0005-1098(82)90026-7","mag":"1994100237"},"language":"en","primary_location":{"id":"doi:10.1016/0005-1098(82)90026-7","is_oa":false,"landing_page_url":"https://doi.org/10.1016/0005-1098(82)90026-7","pdf_url":null,"source":{"id":"https://openalex.org/S51360982","display_name":"Automatica","issn_l":"0005-1098","issn":["0005-1098","1873-2836"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Automatica","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/A5103692639","display_name":"Bruce A. Francis","orcid":null},"institutions":[{"id":"https://openalex.org/I151746483","display_name":"University of Waterloo","ror":"https://ror.org/01aff2v68","country_code":"CA","type":"education","lineage":["https://openalex.org/I151746483"]}],"countries":["CA"],"is_corresponding":true,"raw_author_name":"Bruce A. Francis","raw_affiliation_strings":["Department of Electrical Engineering, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada"],"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada","institution_ids":["https://openalex.org/I151746483"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5103692639"],"corresponding_institution_ids":["https://openalex.org/I151746483"],"apc_list":{"value":3500,"currency":"USD","value_usd":3500},"apc_paid":null,"fwci":8.1172,"has_fulltext":false,"cited_by_count":31,"citation_normalized_percentile":{"value":0.97681607,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"18","issue":"1","first_page":"57","last_page":"62"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12727","display_name":"Differential Equations and Numerical Methods","score":0.9998999834060669,"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/T12727","display_name":"Differential Equations and Numerical Methods","score":0.9998999834060669,"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/T11416","display_name":"Numerical methods for differential equations","score":0.9901999831199646,"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/T10173","display_name":"Computational Fluid Dynamics and Aerodynamics","score":0.979200005531311,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7188785672187805},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.6925116181373596},{"id":"https://openalex.org/keywords/ordinary-differential-equation","display_name":"Ordinary differential equation","score":0.6638498306274414},{"id":"https://openalex.org/keywords/limiting","display_name":"Limiting","score":0.5525571703910828},{"id":"https://openalex.org/keywords/linear-quadratic-regulator","display_name":"Linear-quadratic regulator","score":0.5510606169700623},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5119749307632446},{"id":"https://openalex.org/keywords/sense","display_name":"Sense (electronics)","score":0.4893497824668884},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.46495991945266724},{"id":"https://openalex.org/keywords/optimal-control","display_name":"Optimal control","score":0.46450161933898926},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.46264421939849854},{"id":"https://openalex.org/keywords/linear-system","display_name":"Linear system","score":0.4469505846500397},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.43863019347190857},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.42752790451049805},{"id":"https://openalex.org/keywords/distribution","display_name":"Distribution (mathematics)","score":0.4222654700279236},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.38618162274360657},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.3694390654563904},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.21344873309135437},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.1987166404724121},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.13470163941383362},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.09115862846374512},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.0751703679561615}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7188785672187805},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.6925116181373596},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.6638498306274414},{"id":"https://openalex.org/C188198153","wikidata":"https://www.wikidata.org/wiki/Q1613840","display_name":"Limiting","level":2,"score":0.5525571703910828},{"id":"https://openalex.org/C98779006","wikidata":"https://www.wikidata.org/wiki/Q2520550","display_name":"Linear-quadratic regulator","level":3,"score":0.5510606169700623},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5119749307632446},{"id":"https://openalex.org/C143141573","wikidata":"https://www.wikidata.org/wiki/Q7450971","display_name":"Sense (electronics)","level":2,"score":0.4893497824668884},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.46495991945266724},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.46450161933898926},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.46264421939849854},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.4469505846500397},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.43863019347190857},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.42752790451049805},{"id":"https://openalex.org/C110121322","wikidata":"https://www.wikidata.org/wiki/Q865811","display_name":"Distribution (mathematics)","level":2,"score":0.4222654700279236},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.38618162274360657},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.3694390654563904},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.21344873309135437},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.1987166404724121},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.13470163941383362},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.09115862846374512},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0751703679561615},{"id":"https://openalex.org/C119599485","wikidata":"https://www.wikidata.org/wiki/Q43035","display_name":"Electrical engineering","level":1,"score":0.0},{"id":"https://openalex.org/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical engineering","level":1,"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/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1016/0005-1098(82)90026-7","is_oa":false,"landing_page_url":"https://doi.org/10.1016/0005-1098(82)90026-7","pdf_url":null,"source":{"id":"https://openalex.org/S51360982","display_name":"Automatica","issn_l":"0005-1098","issn":["0005-1098","1873-2836"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Automatica","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":15,"referenced_works":["https://openalex.org/W1490039160","https://openalex.org/W1556970733","https://openalex.org/W1965640670","https://openalex.org/W1989323519","https://openalex.org/W1991914862","https://openalex.org/W1997665618","https://openalex.org/W2005986740","https://openalex.org/W2045402759","https://openalex.org/W2062361291","https://openalex.org/W2070623399","https://openalex.org/W2102628180","https://openalex.org/W2115251312","https://openalex.org/W2122821164","https://openalex.org/W3003197133","https://openalex.org/W6651867753"],"related_works":["https://openalex.org/W4385542742","https://openalex.org/W2037111888","https://openalex.org/W3170014661","https://openalex.org/W4391254571","https://openalex.org/W2414034219","https://openalex.org/W2463801224","https://openalex.org/W2203843426","https://openalex.org/W2138713378","https://openalex.org/W2049369111","https://openalex.org/W2151337373"],"abstract_inverted_index":null,"counts_by_year":[{"year":2017,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
