{"id":"https://openalex.org/W2015562476","doi":"https://doi.org/10.1137/1032079","title":"A Numerical and Asymptotic Study of Some Third-Order Ordinary Differential Equations Relevant to Draining and Coating Flows","display_name":"A Numerical and Asymptotic Study of Some Third-Order Ordinary Differential Equations Relevant to Draining and Coating Flows","publication_year":1990,"publication_date":"1990-09-01","ids":{"openalex":"https://openalex.org/W2015562476","doi":"https://doi.org/10.1137/1032079","mag":"2015562476"},"language":"en","primary_location":{"id":"doi:10.1137/1032079","is_oa":false,"landing_page_url":"https://doi.org/10.1137/1032079","pdf_url":null,"source":{"id":"https://openalex.org/S160107561","display_name":"SIAM Review","issn_l":"0036-1445","issn":["0036-1445","1095-7200"],"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":"SIAM Review","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/A5110271625","display_name":"E. O. Tuck","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"E. O. Tuck","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5087116432","display_name":"Leonard W. Schwartz","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"L. W. Schwartz","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":4.5808,"has_fulltext":false,"cited_by_count":214,"citation_normalized_percentile":{"value":0.94762123,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":100},"biblio":{"volume":"32","issue":"3","first_page":"453","last_page":"469"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12141","display_name":"Fluid Dynamics and Thin Films","score":0.9994000196456909,"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"}},"topics":[{"id":"https://openalex.org/T12141","display_name":"Fluid Dynamics and Thin Films","score":0.9994000196456909,"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"}},{"id":"https://openalex.org/T11382","display_name":"Fluid Dynamics and Heat Transfer","score":0.9943000078201294,"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"}},{"id":"https://openalex.org/T10313","display_name":"Surface Modification and Superhydrophobicity","score":0.9922999739646912,"subfield":{"id":"https://openalex.org/subfields/2508","display_name":"Surfaces, Coatings and Films"},"field":{"id":"https://openalex.org/fields/25","display_name":"Materials Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/singularity","display_name":"Singularity","score":0.7601109743118286},{"id":"https://openalex.org/keywords/singular-perturbation","display_name":"Singular perturbation","score":0.6385337114334106},{"id":"https://openalex.org/keywords/ordinary-differential-equation","display_name":"Ordinary differential equation","score":0.6347011923789978},{"id":"https://openalex.org/keywords/limiting","display_name":"Limiting","score":0.5439278483390808},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5426043272018433},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5256903171539307},{"id":"https://openalex.org/keywords/asymptotic-analysis","display_name":"Asymptotic analysis","score":0.48817116022109985},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.48568448424339294},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.45485591888427734},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.4376406669616699}],"concepts":[{"id":"https://openalex.org/C16171025","wikidata":"https://www.wikidata.org/wiki/Q863349","display_name":"Singularity","level":2,"score":0.7601109743118286},{"id":"https://openalex.org/C165160513","wikidata":"https://www.wikidata.org/wiki/Q7524249","display_name":"Singular perturbation","level":2,"score":0.6385337114334106},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.6347011923789978},{"id":"https://openalex.org/C188198153","wikidata":"https://www.wikidata.org/wiki/Q1613840","display_name":"Limiting","level":2,"score":0.5439278483390808},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5426043272018433},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5256903171539307},{"id":"https://openalex.org/C205147927","wikidata":"https://www.wikidata.org/wiki/Q752718","display_name":"Asymptotic analysis","level":2,"score":0.48817116022109985},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.48568448424339294},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.45485591888427734},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.4376406669616699},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","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/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical engineering","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/1032079","is_oa":false,"landing_page_url":"https://doi.org/10.1137/1032079","pdf_url":null,"source":{"id":"https://openalex.org/S160107561","display_name":"SIAM Review","issn_l":"0036-1445","issn":["0036-1445","1095-7200"],"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":"SIAM Review","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":26,"referenced_works":["https://openalex.org/W144372291","https://openalex.org/W1986391085","https://openalex.org/W2003508639","https://openalex.org/W2004544770","https://openalex.org/W2006699869","https://openalex.org/W2008600717","https://openalex.org/W2009343422","https://openalex.org/W2022809927","https://openalex.org/W2026245731","https://openalex.org/W2027502822","https://openalex.org/W2033628198","https://openalex.org/W2046770317","https://openalex.org/W2052466660","https://openalex.org/W2084732309","https://openalex.org/W2102204567","https://openalex.org/W2107134869","https://openalex.org/W2115463092","https://openalex.org/W2115619789","https://openalex.org/W2121836593","https://openalex.org/W2155788949","https://openalex.org/W2564484726","https://openalex.org/W2997010975","https://openalex.org/W4233126315","https://openalex.org/W4236857656","https://openalex.org/W4240078066","https://openalex.org/W4244292591"],"related_works":["https://openalex.org/W2125893105","https://openalex.org/W1994904484","https://openalex.org/W2012779601","https://openalex.org/W624943865","https://openalex.org/W1982045356","https://openalex.org/W2380014550","https://openalex.org/W1994025175","https://openalex.org/W2512446078","https://openalex.org/W2375302685","https://openalex.org/W2065671108"],"abstract_inverted_index":{"Some":[0],"draining":[1,65,122],"or":[2],"coating":[3],"fluid-flow":[4],"problems,":[5],"in":[6,98],"which":[7,106],"surface":[8],"tension":[9],"forces":[10],"are":[11,23,130,188],"important,":[12],"can":[13],"be":[14],"described":[15],"by":[16,185],"third-order":[17],"ordinary":[18],"differential":[19],"equations.":[20],"Accurate":[21],"computations":[22],"provided":[24],"here":[25],"for":[26,78,83,137,162],"examples":[27],"such":[28,92,108],"as":[29,47,73,101,114],"$y'''(x)":[30],"=":[31,151,157],"-":[32,50],"1":[33],"+":[34,117],"{1":[35],"/":[36],"{y^2":[37],"}}$":[38],"that":[39,59,93,109,181],"permit":[40,155],"the":[41,64,71,79,99,147,166,183],"boundary":[42],"condition":[43],"$y":[44,110,156],"\\to":[45,49,103,111,116],"1$":[46],"$x":[48,115],"\\infty":[51,118],"$,":[52,119,140],"so":[53,120],"modelling":[54,121],"a":[55,84,87,143,171,175],"layer":[56],"of":[57,70,169],"fluid":[58],"is":[60,76,96,107,165],"asymptotically":[61],"uniform":[62],"behind":[63],"front.":[66],"The":[67,159],"ultimate":[68],"fate":[69],"solution":[72],"x":[74],"increases":[75],"studied":[77],"above":[80],"example,":[81],"and":[82],"generalisation":[85],"involving":[86],"small":[88,138],"parameter":[89],"$\\delta":[90,102,139,150],"$":[91,113],"this":[94,141,163],"example":[95],"recovered":[97],"limit":[100],"0$,":[104],"but":[105],"\\delta":[112],"over":[123,174],"an":[124],"already-wet":[125],"surface.":[126,178],"Matched":[127],"asymptotic":[128],"expansions":[129],"then":[131],"used":[132],"to":[133],"derive":[134],"limiting":[135],"results":[136],"being":[142],"singular":[144],"perturbation":[145],"since":[146],"problem":[148],"with":[149],"0$":[152],"does":[153],"not":[154],"0$.":[158],"physical":[160],"basis":[161],"singularity":[164,184],"well-known":[167],"impossibility":[168],"moving":[170],"contact":[172],"line":[173],"dry":[176],"nonslip":[177],"Other":[179],"modifications":[180],"avoid":[182],"allowing":[186],"slip":[187],"also":[189],"discussed.":[190]},"counts_by_year":[{"year":2026,"cited_by_count":4},{"year":2025,"cited_by_count":8},{"year":2024,"cited_by_count":6},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":10},{"year":2020,"cited_by_count":7},{"year":2019,"cited_by_count":6},{"year":2018,"cited_by_count":4},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":5},{"year":2015,"cited_by_count":4},{"year":2014,"cited_by_count":8},{"year":2013,"cited_by_count":6},{"year":2012,"cited_by_count":14}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}