{"id":"https://openalex.org/W2591853258","doi":"https://doi.org/10.1137/040603577","title":"Fast and Slow Dynamics for the Computational Singular Perturbation Method","display_name":"Fast and Slow Dynamics for the Computational Singular Perturbation Method","publication_year":2004,"publication_date":"2004-01-01","ids":{"openalex":"https://openalex.org/W2591853258","doi":"https://doi.org/10.1137/040603577","mag":"2591853258"},"language":"en","primary_location":{"id":"doi:10.1137/040603577","is_oa":false,"landing_page_url":"https://doi.org/10.1137/040603577","pdf_url":null,"source":{"id":"https://openalex.org/S4357572","display_name":"Multiscale Modeling and Simulation","issn_l":"1540-3459","issn":["1540-3459","1540-3467"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Multiscale Modeling & Simulation","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/A5068154289","display_name":"Antonios Zagaris","orcid":"https://orcid.org/0000-0001-6646-0390"},"institutions":[{"id":"https://openalex.org/I111088046","display_name":"Boston University","ror":"https://ror.org/05qwgg493","country_code":"US","type":"education","lineage":["https://openalex.org/I111088046"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Antonios Zagaris","raw_affiliation_strings":["Department of Mathematics and Center for BioDynamics Boston University, Boston, Massachusetts, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Center for BioDynamics Boston University, Boston, Massachusetts, USA","institution_ids":["https://openalex.org/I111088046"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5054755754","display_name":"Hans G. Kaper","orcid":"https://orcid.org/0000-0003-1154-2406"},"institutions":[{"id":"https://openalex.org/I1282105669","display_name":"Argonne National Laboratory","ror":"https://ror.org/05gvnxz63","country_code":"US","type":"facility","lineage":["https://openalex.org/I1282105669","https://openalex.org/I1330989302","https://openalex.org/I39565521","https://openalex.org/I40347166"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Hans G. Kaper","raw_affiliation_strings":["Mathematics and Computer Science Division, Argonne National Laboratory, Argonne, Illinois, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Mathematics and Computer Science Division, Argonne National Laboratory, Argonne, Illinois, USA","institution_ids":["https://openalex.org/I1282105669"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5087776335","display_name":"Tasso J. Kaper","orcid":"https://orcid.org/0000-0003-0028-6865"},"institutions":[{"id":"https://openalex.org/I111088046","display_name":"Boston University","ror":"https://ror.org/05qwgg493","country_code":"US","type":"education","lineage":["https://openalex.org/I111088046"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Tasso J. Kaper","raw_affiliation_strings":["Department of Mathematics and Center for BioDynamics Boston University, Boston, Massachusetts, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Center for BioDynamics Boston University, Boston, Massachusetts, USA","institution_ids":["https://openalex.org/I111088046"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5068154289"],"corresponding_institution_ids":["https://openalex.org/I111088046"],"apc_list":null,"apc_paid":null,"fwci":6.0429,"has_fulltext":false,"cited_by_count":93,"citation_normalized_percentile":{"value":0.967342,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"2","issue":"4","first_page":"613","last_page":"638"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12727","display_name":"Differential Equations and Numerical Methods","score":0.9991999864578247,"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":0.9991999864578247,"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":0.9937000274658203,"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":0.9904000163078308,"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/slow-manifold","display_name":"Slow manifold","score":0.8894820213317871},{"id":"https://openalex.org/keywords/curse-of-dimensionality","display_name":"Curse of dimensionality","score":0.7145746946334839},{"id":"https://openalex.org/keywords/singular-perturbation","display_name":"Singular perturbation","score":0.6953772306442261},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6604639291763306},{"id":"https://openalex.org/keywords/tangent-space","display_name":"Tangent space","score":0.6455485820770264},{"id":"https://openalex.org/keywords/tangent","display_name":"Tangent","score":0.5927534103393555},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5593887567520142},{"id":"https://openalex.org/keywords/manifold","display_name":"Manifold (fluid mechanics)","score":0.5431318879127502},{"id":"https://openalex.org/keywords/iterative-method","display_name":"Iterative method","score":0.5132772922515869},{"id":"https://openalex.org/keywords/perturbation","display_name":"Perturbation (astronomy)","score":0.4842681288719177},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.44736623764038086},{"id":"https://openalex.org/keywords/ordinary-differential-equation","display_name":"Ordinary differential equation","score":0.42081204056739807},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3804565668106079},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.3622826337814331},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.2808099091053009},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.1088898777961731},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.07987213134765625}],"concepts":[{"id":"https://openalex.org/C2778671503","wikidata":"https://www.wikidata.org/wiki/Q7542110","display_name":"Slow manifold","level":3,"score":0.8894820213317871},{"id":"https://openalex.org/C111030470","wikidata":"https://www.wikidata.org/wiki/Q1430460","display_name":"Curse of dimensionality","level":2,"score":0.7145746946334839},{"id":"https://openalex.org/C165160513","wikidata":"https://www.wikidata.org/wiki/Q7524249","display_name":"Singular perturbation","level":2,"score":0.6953772306442261},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6604639291763306},{"id":"https://openalex.org/C157157409","wikidata":"https://www.wikidata.org/wiki/Q909601","display_name":"Tangent space","level":2,"score":0.6455485820770264},{"id":"https://openalex.org/C138187205","wikidata":"https://www.wikidata.org/wiki/Q131251","display_name":"Tangent","level":2,"score":0.5927534103393555},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5593887567520142},{"id":"https://openalex.org/C529865628","wikidata":"https://www.wikidata.org/wiki/Q1790740","display_name":"Manifold (fluid mechanics)","level":2,"score":0.5431318879127502},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.5132772922515869},{"id":"https://openalex.org/C177918212","wikidata":"https://www.wikidata.org/wiki/Q803623","display_name":"Perturbation (astronomy)","level":2,"score":0.4842681288719177},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.44736623764038086},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.42081204056739807},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3804565668106079},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.3622826337814331},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.2808099091053009},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.1088898777961731},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.07987213134765625},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","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/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/040603577","is_oa":false,"landing_page_url":"https://doi.org/10.1137/040603577","pdf_url":null,"source":{"id":"https://openalex.org/S4357572","display_name":"Multiscale Modeling and Simulation","issn_l":"1540-3459","issn":["1540-3459","1540-3467"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Multiscale Modeling & Simulation","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G3892653051","display_name":null,"funder_award_id":"W-31-109-Eng-38","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320306084","display_name":"U.S. Department of Energy","ror":"https://ror.org/01bj3aw27"},{"id":"https://openalex.org/F4320337380","display_name":"Division of Mathematical Sciences","ror":"https://ror.org/051fftw81"},{"id":"https://openalex.org/F4320337506","display_name":"Advanced Scientific Computing Research","ror":"https://ror.org/0012c7r22"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":33,"referenced_works":["https://openalex.org/W99189181","https://openalex.org/W200565028","https://openalex.org/W1573927207","https://openalex.org/W1966113499","https://openalex.org/W1991418841","https://openalex.org/W1997508985","https://openalex.org/W1997586090","https://openalex.org/W2001698066","https://openalex.org/W2002164453","https://openalex.org/W2016767879","https://openalex.org/W2024056314","https://openalex.org/W2030787381","https://openalex.org/W2035502912","https://openalex.org/W2036752995","https://openalex.org/W2044431968","https://openalex.org/W2044484168","https://openalex.org/W2050306906","https://openalex.org/W2056372659","https://openalex.org/W2061141488","https://openalex.org/W2061599006","https://openalex.org/W2070233611","https://openalex.org/W2070959866","https://openalex.org/W2071683274","https://openalex.org/W2091182946","https://openalex.org/W2132495809","https://openalex.org/W2138278836","https://openalex.org/W2141906015","https://openalex.org/W2167635580","https://openalex.org/W2577509673","https://openalex.org/W2621042031","https://openalex.org/W4205582579","https://openalex.org/W4229672964","https://openalex.org/W4253802641"],"related_works":["https://openalex.org/W1965619029","https://openalex.org/W1994904484","https://openalex.org/W4297450204","https://openalex.org/W2949645559","https://openalex.org/W2034091978","https://openalex.org/W2591853258","https://openalex.org/W2385244663","https://openalex.org/W2019117083","https://openalex.org/W2179649691","https://openalex.org/W2163618991"],"abstract_inverted_index":{"The":[0],"computational":[1],"singular":[2],"perturbation":[3],"(CSP)":[4],"method":[5,12,67],"ofLam":[6],"and":[7],"Goussis":[8],"is":[9,62,102],"an":[10],"iterative":[11],"to":[13,73,81],"reduce":[14],"the":[15,35,45,49,52,65,70,74,82,96,99,110],"dimensionality":[16],"of":[17,19,37,44,51,91,98],"systems":[18],"ordinary":[20],"differential":[21],"equations":[22],"with":[23],"multiple":[24],"time":[25],"scales.":[26],"In":[27,58,93],"[J.":[28],"Nonlinear":[29],"Sci.,":[30],"14":[31],"(2004),":[32],"pp.":[33],"59--91],":[34],"authors":[36],"this":[38,59],"paper":[39],"showed":[40],"that":[41,64],"each":[42,86],"iteration":[43,87],"CSP":[46,66,100],"algorithm":[47,101],"improves":[48],"approximation":[50],"slow":[53,83,111],"manifold":[54,112],"by":[55,104],"one":[56,89],"order.":[57],"paper,":[60],"it":[61],"shown":[63],"simultaneously":[68],"approximates":[69],"tangent":[71,116],"spaces":[72],"fast":[75],"fibers":[76],"along":[77,113],"which":[78],"solutions":[79],"relax":[80],"manifold.":[84],"Again,":[85],"adds":[88],"order":[90],"accuracy.":[92],"some":[94],"studies,":[95],"output":[97],"postprocessed":[103],"linearly":[105],"projecting":[106],"initial":[107],"data":[108],"onto":[109],"these":[114],"approximate":[115],"spaces.":[117],"These":[118],"projections,":[119],"in":[120],"turn,":[121],"also":[122],"become":[123],"successively":[124],"more":[125],"accurate.":[126]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":8},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":8},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":7},{"year":2014,"cited_by_count":5},{"year":2013,"cited_by_count":7},{"year":2012,"cited_by_count":3}],"updated_date":"2026-05-23T08:51:43.019350","created_date":"2025-10-10T00:00:00"}