{"id":"https://openalex.org/W2624475384","doi":"https://doi.org/10.1080/00207160.2017.1339869","title":"A high-order finite difference scheme for a singularly perturbed fourth-order ordinary differential equation","display_name":"A high-order finite difference scheme for a singularly perturbed fourth-order ordinary differential equation","publication_year":2017,"publication_date":"2017-06-09","ids":{"openalex":"https://openalex.org/W2624475384","doi":"https://doi.org/10.1080/00207160.2017.1339869","mag":"2624475384"},"language":"en","primary_location":{"id":"doi:10.1080/00207160.2017.1339869","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207160.2017.1339869","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":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5003721958","display_name":"Zhongdi Cen","orcid":"https://orcid.org/0000-0001-9739-2036"},"institutions":[{"id":"https://openalex.org/I1315279114","display_name":"Zhejiang Wanli University","ror":"https://ror.org/00rjdhd62","country_code":"CN","type":"education","lineage":["https://openalex.org/I1315279114"]},{"id":"https://openalex.org/I4210088000","display_name":"Ningbo Dahongying University","ror":"https://ror.org/0085x3f43","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210088000"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zhongdi Cen","raw_affiliation_strings":["College of Finance and Trade, Ningbo Dahongying University, Ningbo, Zhejiang, China","Institute of Mathematics, Zhejiang Wanli University, Ningbo, Zhejiang, China"],"affiliations":[{"raw_affiliation_string":"College of Finance and Trade, Ningbo Dahongying University, Ningbo, Zhejiang, China","institution_ids":["https://openalex.org/I4210088000"]},{"raw_affiliation_string":"Institute of Mathematics, Zhejiang Wanli University, Ningbo, Zhejiang, China","institution_ids":["https://openalex.org/I1315279114"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100523812","display_name":"Aimin Xu","orcid":null},"institutions":[{"id":"https://openalex.org/I1315279114","display_name":"Zhejiang Wanli University","ror":"https://ror.org/00rjdhd62","country_code":"CN","type":"education","lineage":["https://openalex.org/I1315279114"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Aimin Xu","raw_affiliation_strings":["Institute of Mathematics, Zhejiang Wanli University, Ningbo, Zhejiang, China"],"affiliations":[{"raw_affiliation_string":"Institute of Mathematics, Zhejiang Wanli University, Ningbo, Zhejiang, China","institution_ids":["https://openalex.org/I1315279114"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5037356512","display_name":"Anbo Le","orcid":"https://orcid.org/0000-0003-0366-2408"},"institutions":[{"id":"https://openalex.org/I1315279114","display_name":"Zhejiang Wanli University","ror":"https://ror.org/00rjdhd62","country_code":"CN","type":"education","lineage":["https://openalex.org/I1315279114"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Anbo Le","raw_affiliation_strings":["Institute of Mathematics, Zhejiang Wanli University, Ningbo, Zhejiang, China"],"affiliations":[{"raw_affiliation_string":"Institute of Mathematics, Zhejiang Wanli University, Ningbo, Zhejiang, China","institution_ids":["https://openalex.org/I1315279114"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5037356512"],"corresponding_institution_ids":["https://openalex.org/I1315279114"],"apc_list":null,"apc_paid":null,"fwci":0.3545,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.5444664,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"95","issue":"9","first_page":"1806","last_page":"1819"},"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/T11416","display_name":"Numerical methods for differential equations","score":0.9326000213623047,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.90060955286026},{"id":"https://openalex.org/keywords/equidistant","display_name":"Equidistant","score":0.6694979667663574},{"id":"https://openalex.org/keywords/ordinary-differential-equation","display_name":"Ordinary differential equation","score":0.6566369533538818},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.6256181597709656},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5615947246551514},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.5545616149902344},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.517917811870575},{"id":"https://openalex.org/keywords/singular-perturbation","display_name":"Singular perturbation","score":0.5056688785552979},{"id":"https://openalex.org/keywords/finite-difference-scheme","display_name":"Finite difference scheme","score":0.47517555952072144},{"id":"https://openalex.org/keywords/finite-difference-method","display_name":"Finite difference method","score":0.45487675070762634},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.45089957118034363},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3662850856781006},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.10112959146499634}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.90060955286026},{"id":"https://openalex.org/C158245278","wikidata":"https://www.wikidata.org/wiki/Q4386982","display_name":"Equidistant","level":2,"score":0.6694979667663574},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.6566369533538818},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.6256181597709656},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5615947246551514},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.5545616149902344},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.517917811870575},{"id":"https://openalex.org/C165160513","wikidata":"https://www.wikidata.org/wiki/Q7524249","display_name":"Singular perturbation","level":2,"score":0.5056688785552979},{"id":"https://openalex.org/C2988766672","wikidata":"https://www.wikidata.org/wiki/Q1147751","display_name":"Finite difference scheme","level":2,"score":0.47517555952072144},{"id":"https://openalex.org/C205951836","wikidata":"https://www.wikidata.org/wiki/Q1147751","display_name":"Finite difference method","level":2,"score":0.45487675070762634},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.45089957118034363},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3662850856781006},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.10112959146499634},{"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/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/00207160.2017.1339869","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207160.2017.1339869","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G3157558763","display_name":null,"funder_award_id":"2015A610161","funder_id":"https://openalex.org/F4320323225","funder_display_name":"Natural Science Foundation of Ningbo Municipality"}],"funders":[{"id":"https://openalex.org/F4320323225","display_name":"Natural Science Foundation of Ningbo Municipality","ror":"https://ror.org/01h0zpd94"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":20,"referenced_works":["https://openalex.org/W1476132770","https://openalex.org/W1998573164","https://openalex.org/W2013129667","https://openalex.org/W2021426558","https://openalex.org/W2023292440","https://openalex.org/W2024022377","https://openalex.org/W2029838506","https://openalex.org/W2030298437","https://openalex.org/W2057143111","https://openalex.org/W2070535118","https://openalex.org/W2072299097","https://openalex.org/W2076401427","https://openalex.org/W2076408646","https://openalex.org/W2089332477","https://openalex.org/W2115251580","https://openalex.org/W2137516988","https://openalex.org/W2140580049","https://openalex.org/W2144048306","https://openalex.org/W2397082217","https://openalex.org/W4234587664"],"related_works":["https://openalex.org/W2017891420","https://openalex.org/W25939672","https://openalex.org/W2009573643","https://openalex.org/W2066872858","https://openalex.org/W1984946324","https://openalex.org/W4221011345","https://openalex.org/W1984657540","https://openalex.org/W2045633467","https://openalex.org/W4312402136","https://openalex.org/W3096126878"],"abstract_inverted_index":{"In":[0],"this":[1],"paper":[2],"a":[3,18,31,45,48],"singularly":[4,22],"perturbed":[5,23],"fourth-order":[6,99],"ordinary":[7],"differential":[8,13],"equation":[9,14],"is":[10,15,34,44,79,94],"considered.":[11],"The":[12,92],"transformed":[16],"into":[17],"coupled":[19],"system":[20],"of":[21,47,51],"equations.":[24],"A":[25],"hybrid":[26,41],"finite":[27],"difference":[28,42,58,84],"scheme":[29,43,54,59,78,85,93],"on":[30,61],"Vulanovi\u0107\u2013Shishkin":[32],"mesh":[33,67],"used":[35],"to":[36,96],"discretize":[37],"the":[38,52,56,62,65,70,77,83,89,103,113],"system.":[39],"This":[40],"combination":[46],"non-equidistant":[49],"generalization":[50],"Numerov":[53],"and":[55,69],"central":[57],"based":[60],"relation":[63],"between":[64],"local":[66],"widths":[68],"perturbation":[71],"parameter.":[72],"We":[73],"will":[74],"show":[75],"that":[76],"maximum-norm":[80],"stable,":[81],"although":[82],"may":[86],"not":[87],"satisfy":[88],"maximum":[90,105],"principle.":[91],"proved":[95],"be":[97],"almost":[98],"uniformly":[100],"convergent":[101],"in":[102],"discrete":[104],"norm.":[106],"Numerical":[107],"results":[108],"are":[109],"presented":[110],"for":[111],"supporting":[112],"theoretical":[114],"results.":[115]},"counts_by_year":[{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":1},{"year":2020,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}