{"id":"https://openalex.org/W2178962657","doi":"https://doi.org/10.1080/00207160.2015.1076805","title":"Numerical treatment of a quasilinear initial value problem with boundary layer","display_name":"Numerical treatment of a quasilinear initial value problem with boundary layer","publication_year":2015,"publication_date":"2015-07-30","ids":{"openalex":"https://openalex.org/W2178962657","doi":"https://doi.org/10.1080/00207160.2015.1076805","mag":"2178962657"},"language":"en","primary_location":{"id":"doi:10.1080/00207160.2015.1076805","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207160.2015.1076805","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":true,"oa_status":"green","oa_url":"https://acikerisim.duzce.edu.tr/bitstreams/8b9a9c9a-54c0-4bbc-b388-aa2d281ff0b3/download","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5004484743","display_name":"Musa \u00c7ak\u0131r","orcid":"https://orcid.org/0000-0002-1979-570X"},"institutions":[{"id":"https://openalex.org/I118567650","display_name":"Van Y\u00fcz\u00fcnc\u00fc Y\u0131l \u00dcniversitesi","ror":"https://ror.org/041jyzp61","country_code":"TR","type":"education","lineage":["https://openalex.org/I118567650"]}],"countries":["TR"],"is_corresponding":true,"raw_author_name":"Musa Cakir","raw_affiliation_strings":["Department of Mathematics, Faculty of Sciences, Yuzuncu Yil University, 65080 Van, Turkey"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Faculty of Sciences, Yuzuncu Yil University, 65080 Van, Turkey","institution_ids":["https://openalex.org/I118567650"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5038029668","display_name":"Erkan \u00c7imen","orcid":"https://orcid.org/0000-0002-7258-192X"},"institutions":[{"id":"https://openalex.org/I118567650","display_name":"Van Y\u00fcz\u00fcnc\u00fc Y\u0131l \u00dcniversitesi","ror":"https://ror.org/041jyzp61","country_code":"TR","type":"education","lineage":["https://openalex.org/I118567650"]}],"countries":["TR"],"is_corresponding":false,"raw_author_name":"Erkan Cimen","raw_affiliation_strings":["Department of Mathematics, Faculty of Education, Yuzuncu Yil University, 65080 Van, Turkey"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Faculty of Education, Yuzuncu Yil University, 65080 Van, Turkey","institution_ids":["https://openalex.org/I118567650"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5090478805","display_name":"\u0130lhame Amirali","orcid":"https://orcid.org/0000-0002-5103-8856"},"institutions":[{"id":"https://openalex.org/I54001450","display_name":"D\u00fczce \u00dcniversitesi","ror":"https://ror.org/04175wc52","country_code":"TR","type":"education","lineage":["https://openalex.org/I54001450"]}],"countries":["TR"],"is_corresponding":false,"raw_author_name":"Ilhame Amirali","raw_affiliation_strings":["Department of Mathematics, Faculty of Arts and Sciences, Duzce University, 81620 Duzce, Turkey"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Faculty of Arts and Sciences, Duzce University, 81620 Duzce, Turkey","institution_ids":["https://openalex.org/I54001450"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5037065820","display_name":"Gabil M. Amiraliyev","orcid":"https://orcid.org/0000-0001-6585-7353"},"institutions":[{"id":"https://openalex.org/I176037994","display_name":"Erzincan University","ror":"https://ror.org/02h1e8605","country_code":"TR","type":"education","lineage":["https://openalex.org/I176037994"]}],"countries":["TR"],"is_corresponding":false,"raw_author_name":"Gabil M. Amiraliyev","raw_affiliation_strings":["Department of Mathematics, Faculty of Arts and Sciences, Erzincan University, 24000 Erzincan, Turkey"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Faculty of Arts and Sciences, Erzincan University, 24000 Erzincan, Turkey","institution_ids":["https://openalex.org/I176037994"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5004484743"],"corresponding_institution_ids":["https://openalex.org/I118567650"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":7,"citation_normalized_percentile":{"value":0.1092056,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"93","issue":"11","first_page":"1845","last_page":"1859"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12727","display_name":"Differential Equations and Numerical Methods","score":1.0,"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":1.0,"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/T13685","display_name":"Material Science and Thermodynamics","score":0.9430000185966492,"subfield":{"id":"https://openalex.org/subfields/2210","display_name":"Mechanical 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/T12589","display_name":"Differential Equations and Boundary Problems","score":0.9366999864578247,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.876159131526947},{"id":"https://openalex.org/keywords/piecewise","display_name":"Piecewise","score":0.6543619632720947},{"id":"https://openalex.org/keywords/logarithm","display_name":"Logarithm","score":0.5783056020736694},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.5658095479011536},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.5423712134361267},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5423156023025513},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.5383134484291077},{"id":"https://openalex.org/keywords/initial-value-problem","display_name":"Initial value problem","score":0.5364642143249512},{"id":"https://openalex.org/keywords/singular-perturbation","display_name":"Singular perturbation","score":0.5043095350265503},{"id":"https://openalex.org/keywords/perturbation","display_name":"Perturbation (astronomy)","score":0.4395110011100769},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4343945384025574}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.876159131526947},{"id":"https://openalex.org/C164660894","wikidata":"https://www.wikidata.org/wiki/Q2037833","display_name":"Piecewise","level":2,"score":0.6543619632720947},{"id":"https://openalex.org/C39927690","wikidata":"https://www.wikidata.org/wiki/Q11197","display_name":"Logarithm","level":2,"score":0.5783056020736694},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.5658095479011536},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.5423712134361267},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5423156023025513},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.5383134484291077},{"id":"https://openalex.org/C26955809","wikidata":"https://www.wikidata.org/wiki/Q10167591","display_name":"Initial value problem","level":2,"score":0.5364642143249512},{"id":"https://openalex.org/C165160513","wikidata":"https://www.wikidata.org/wiki/Q7524249","display_name":"Singular perturbation","level":2,"score":0.5043095350265503},{"id":"https://openalex.org/C177918212","wikidata":"https://www.wikidata.org/wiki/Q803623","display_name":"Perturbation (astronomy)","level":2,"score":0.4395110011100769},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4343945384025574},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","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},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1080/00207160.2015.1076805","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207160.2015.1076805","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:27d06acb-1c3a-4fb7-b02e-571809f594ac","is_oa":false,"landing_page_url":"https://avesis.yyu.edu.tr/publication/details/27d06acb-1c3a-4fb7-b02e-571809f594ac/oai","pdf_url":null,"source":{"id":"https://openalex.org/S7407055328","display_name":"Van Y\u00fcz\u00fcnc\u00fc Y\u0131l University Academic Data Management System","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":null,"raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:acikerisim.duzce.edu.tr:20.500.12684/3849","is_oa":true,"landing_page_url":"https://acikerisim.duzce.edu.tr/bitstreams/8b9a9c9a-54c0-4bbc-b388-aa2d281ff0b3/download","pdf_url":null,"source":{"id":"https://openalex.org/S4377196355","display_name":"DSpace - D\u00fczce (Duzce University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I54001450","host_organization_name":"D\u00fczce \u00dcniversitesi","host_organization_lineage":["https://openalex.org/I54001450"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"article"}],"best_oa_location":{"id":"pmh:oai:acikerisim.duzce.edu.tr:20.500.12684/3849","is_oa":true,"landing_page_url":"https://acikerisim.duzce.edu.tr/bitstreams/8b9a9c9a-54c0-4bbc-b388-aa2d281ff0b3/download","pdf_url":null,"source":{"id":"https://openalex.org/S4377196355","display_name":"DSpace - D\u00fczce (Duzce University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I54001450","host_organization_name":"D\u00fczce \u00dcniversitesi","host_organization_lineage":["https://openalex.org/I54001450"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":38,"referenced_works":["https://openalex.org/W159802412","https://openalex.org/W603226872","https://openalex.org/W1476132770","https://openalex.org/W1511461612","https://openalex.org/W1524707262","https://openalex.org/W1664493768","https://openalex.org/W1958809597","https://openalex.org/W1966774412","https://openalex.org/W1976141150","https://openalex.org/W1977795067","https://openalex.org/W1986034894","https://openalex.org/W1986353141","https://openalex.org/W1988666001","https://openalex.org/W1996536528","https://openalex.org/W1999928604","https://openalex.org/W2003812329","https://openalex.org/W2007208452","https://openalex.org/W2021272693","https://openalex.org/W2028770876","https://openalex.org/W2034388696","https://openalex.org/W2047131285","https://openalex.org/W2063998193","https://openalex.org/W2073668569","https://openalex.org/W2076408646","https://openalex.org/W2083491866","https://openalex.org/W2085832119","https://openalex.org/W2085899990","https://openalex.org/W2086201809","https://openalex.org/W2088410534","https://openalex.org/W2117954199","https://openalex.org/W2129349371","https://openalex.org/W2154078774","https://openalex.org/W2155728152","https://openalex.org/W2161502942","https://openalex.org/W2487775498","https://openalex.org/W2493736762","https://openalex.org/W4235931046","https://openalex.org/W4252247111"],"related_works":["https://openalex.org/W2952185452","https://openalex.org/W2385263368","https://openalex.org/W2798106756","https://openalex.org/W2046736294","https://openalex.org/W2347422947","https://openalex.org/W2061292372","https://openalex.org/W2980815195","https://openalex.org/W4293584968","https://openalex.org/W2071155035","https://openalex.org/W2085466143"],"abstract_inverted_index":{"The":[0,31],"paper":[1],"deals":[2],"with":[3,39],"the":[4,15,35,40,60,71,77,84],"singularly":[5],"perturbed":[6],"quasilinear":[7],"initial":[8,12],"value":[9],"problem":[10,21,36],"exhibiting":[11],"layer.":[13],"First":[14],"nature":[16],"of":[17,19,34,42,76],"solution":[18,28,33],"differential":[20],"before":[22],"presenting":[23],"method":[24,61],"for":[25,66],"its":[26],"numerical":[27,32,81],"is":[29,37,62],"discussed.":[30],"performed":[38],"use":[41],"a":[43,67],"finite-fitted":[44],"difference":[45],"scheme":[46],"on":[47],"an":[48],"appropriate":[49],"piecewise":[50],"uniform":[51],"mesh":[52],"(Shishkin-type":[53],"mesh).":[54],"An":[55],"error":[56],"analysis":[57],"shows":[58],"that":[59],"first-order":[63],"convergent":[64],"except":[65],"logarithmic":[68],"factor,":[69],"in":[70],"discrete":[72],"maximum":[73],"norm,":[74],"independently":[75],"perturbation":[78],"parameter.":[79],"Finally,":[80],"results":[82],"supporting":[83],"theory":[85],"are":[86],"presented.":[87]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":1}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2025-10-10T00:00:00"}
