{"id":"https://openalex.org/W4281685308","doi":"https://doi.org/10.1007/s12190-022-01757-4","title":"An efficient numerical method for a singularly perturbed Fredholm integro-differential equation with integral boundary condition","display_name":"An efficient numerical method for a singularly perturbed Fredholm integro-differential equation with integral boundary condition","publication_year":2022,"publication_date":"2022-06-09","ids":{"openalex":"https://openalex.org/W4281685308","doi":"https://doi.org/10.1007/s12190-022-01757-4","pmid":"https://pubmed.ncbi.nlm.nih.gov/35698573"},"language":"en","primary_location":{"id":"doi:10.1007/s12190-022-01757-4","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s12190-022-01757-4","pdf_url":"https://link.springer.com/content/pdf/10.1007/s12190-022-01757-4.pdf","source":{"id":"https://openalex.org/S199913245","display_name":"Journal of Applied Mathematics and Computing","issn_l":"1598-5865","issn":["1598-5865","1865-2085"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied Mathematics and Computing","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","pubmed"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://link.springer.com/content/pdf/10.1007/s12190-022-01757-4.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5001468512","display_name":"Muhammet Enes Durmaz","orcid":"https://orcid.org/0000-0002-6216-1032"},"institutions":[{"id":"https://openalex.org/I264262938","display_name":"K\u0131rklareli University","ror":"https://ror.org/00jb0e673","country_code":"TR","type":"education","lineage":["https://openalex.org/I264262938"]}],"countries":["TR"],"is_corresponding":true,"raw_author_name":"Muhammet Enes Durmaz","raw_affiliation_strings":["Department of Information Technology, K\u0131rklareli University, K\u0131rklareli, 39100 Turkey","Department of Information Technology, K\u0131rklareli University, K\u0131rklareli, 39100, Turkey"],"affiliations":[{"raw_affiliation_string":"Department of Information Technology, K\u0131rklareli University, K\u0131rklareli, 39100 Turkey","institution_ids":[]},{"raw_affiliation_string":"Department of Information Technology, K\u0131rklareli University, K\u0131rklareli, 39100, Turkey","institution_ids":["https://openalex.org/I264262938"]}]},{"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, D\u00fczce University, D\u00fczce, 81620 Turkey","Department of Mathematics, Faculty of Arts and Sciences, D\u00fczce University, D\u00fczce, 81620, Turkey"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Faculty of Arts and Sciences, D\u00fczce University, D\u00fczce, 81620 Turkey","institution_ids":[]},{"raw_affiliation_string":"Department of Mathematics, Faculty of Arts and Sciences, D\u00fczce University, D\u00fczce, 81620, 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 Binali Y\u0131ld\u0131r\u0131m University, Erzincan, 24100 Turkey","Department of Mathematics, Faculty of Arts and Sciences, Erzincan Binali Y\u0131ld\u0131r\u0131m University, Erzincan, 24100, Turkey"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Faculty of Arts and Sciences, Erzincan Binali Y\u0131ld\u0131r\u0131m University, Erzincan, 24100 Turkey","institution_ids":[]},{"raw_affiliation_string":"Department of Mathematics, Faculty of Arts and Sciences, Erzincan Binali Y\u0131ld\u0131r\u0131m University, Erzincan, 24100, Turkey","institution_ids":["https://openalex.org/I176037994"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5001468512"],"corresponding_institution_ids":["https://openalex.org/I264262938"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":null,"fwci":7.6593,"has_fulltext":true,"cited_by_count":24,"citation_normalized_percentile":{"value":0.98719212,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":91,"max":99},"biblio":{"volume":"69","issue":"1","first_page":"505","last_page":"528"},"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/T12589","display_name":"Differential Equations and Boundary Problems","score":0.977400004863739,"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"}},{"id":"https://openalex.org/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9743000268936157,"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":0.916633129119873},{"id":"https://openalex.org/keywords/fredholm-integral-equation","display_name":"Fredholm integral equation","score":0.7369716167449951},{"id":"https://openalex.org/keywords/fredholm-theory","display_name":"Fredholm theory","score":0.6575042605400085},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.6258899569511414},{"id":"https://openalex.org/keywords/theory-of-computation","display_name":"Theory of computation","score":0.6234760284423828},{"id":"https://openalex.org/keywords/integro-differential-equation","display_name":"Integro-differential equation","score":0.613909900188446},{"id":"https://openalex.org/keywords/integral-equation","display_name":"Integral equation","score":0.6133649945259094},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5979098677635193},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.4747507870197296},{"id":"https://openalex.org/keywords/uniform-convergence","display_name":"Uniform convergence","score":0.467204749584198},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.45271241664886475},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.44266051054000854},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.07656529545783997},{"id":"https://openalex.org/keywords/first-order-partial-differential-equation","display_name":"First-order partial differential equation","score":0.0706949532032013}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.916633129119873},{"id":"https://openalex.org/C89285879","wikidata":"https://www.wikidata.org/wiki/Q2991898","display_name":"Fredholm integral equation","level":3,"score":0.7369716167449951},{"id":"https://openalex.org/C518188847","wikidata":"https://www.wikidata.org/wiki/Q4455098","display_name":"Fredholm theory","level":4,"score":0.6575042605400085},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.6258899569511414},{"id":"https://openalex.org/C24858836","wikidata":"https://www.wikidata.org/wiki/Q844718","display_name":"Theory of computation","level":2,"score":0.6234760284423828},{"id":"https://openalex.org/C70985411","wikidata":"https://www.wikidata.org/wiki/Q2380676","display_name":"Integro-differential equation","level":4,"score":0.613909900188446},{"id":"https://openalex.org/C27016315","wikidata":"https://www.wikidata.org/wiki/Q580101","display_name":"Integral equation","level":2,"score":0.6133649945259094},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5979098677635193},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.4747507870197296},{"id":"https://openalex.org/C157709441","wikidata":"https://www.wikidata.org/wiki/Q1411887","display_name":"Uniform convergence","level":3,"score":0.467204749584198},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.45271241664886475},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.44266051054000854},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.07656529545783997},{"id":"https://openalex.org/C64057670","wikidata":"https://www.wikidata.org/wiki/Q4381442","display_name":"First-order partial differential equation","level":3,"score":0.0706949532032013},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","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/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.0},{"id":"https://openalex.org/C2776257435","wikidata":"https://www.wikidata.org/wiki/Q1576430","display_name":"Bandwidth (computing)","level":2,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1007/s12190-022-01757-4","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s12190-022-01757-4","pdf_url":"https://link.springer.com/content/pdf/10.1007/s12190-022-01757-4.pdf","source":{"id":"https://openalex.org/S199913245","display_name":"Journal of Applied Mathematics and Computing","issn_l":"1598-5865","issn":["1598-5865","1865-2085"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied Mathematics and Computing","raw_type":"journal-article"},{"id":"pmid:35698573","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/35698573","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of applied mathematics & computing","raw_type":null},{"id":"pmh:oai:acikerisim.duzce.edu.tr:20.500.12684/12951","is_oa":true,"landing_page_url":"https://hdl.handle.net/20.500.12684/12951","pdf_url":"https://acikerisim.duzce.edu.tr/bitstreams/f989b7da-c0d6-4a89-8391-c7bc82163d82/download","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"},{"id":"pmh:oai:pubmedcentral.nih.gov:9178336","is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/9178336","pdf_url":null,"source":{"id":"https://openalex.org/S2764455111","display_name":"PubMed Central","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"J Appl Math Comput","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.1007/s12190-022-01757-4","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s12190-022-01757-4","pdf_url":"https://link.springer.com/content/pdf/10.1007/s12190-022-01757-4.pdf","source":{"id":"https://openalex.org/S199913245","display_name":"Journal of Applied Mathematics and Computing","issn_l":"1598-5865","issn":["1598-5865","1865-2085"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied Mathematics and Computing","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4281685308.pdf","grobid_xml":"https://content.openalex.org/works/W4281685308.grobid-xml"},"referenced_works_count":33,"referenced_works":["https://openalex.org/W1476132770","https://openalex.org/W1958809597","https://openalex.org/W1979485793","https://openalex.org/W1981652491","https://openalex.org/W1986728820","https://openalex.org/W2019450558","https://openalex.org/W2040325533","https://openalex.org/W2047426584","https://openalex.org/W2460998628","https://openalex.org/W2522230129","https://openalex.org/W2564083018","https://openalex.org/W2733802133","https://openalex.org/W2803854299","https://openalex.org/W2806761918","https://openalex.org/W2963793984","https://openalex.org/W3090164156","https://openalex.org/W3103681319","https://openalex.org/W3118558494","https://openalex.org/W3127473171","https://openalex.org/W3129772604","https://openalex.org/W3166499094","https://openalex.org/W3167455271","https://openalex.org/W3183398053","https://openalex.org/W3200132617","https://openalex.org/W3203415114","https://openalex.org/W3215106740","https://openalex.org/W3215449623","https://openalex.org/W4205604664","https://openalex.org/W4235931046","https://openalex.org/W4238363765","https://openalex.org/W4245556510","https://openalex.org/W4281685308","https://openalex.org/W6903617359"],"related_works":["https://openalex.org/W1500488077","https://openalex.org/W2001947234","https://openalex.org/W2067960113","https://openalex.org/W2224175176","https://openalex.org/W2493083010","https://openalex.org/W4200421450","https://openalex.org/W2041548793","https://openalex.org/W2141157689","https://openalex.org/W4225900847","https://openalex.org/W4295529414"],"abstract_inverted_index":null,"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":12},{"year":2023,"cited_by_count":9},{"year":2022,"cited_by_count":2}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2025-10-10T00:00:00"}