{"id":"https://openalex.org/W4210776674","doi":"https://doi.org/10.1080/00207160.2022.2037576","title":"Numerical approximations based on sextic B-spline functions for solving fourth-order singular problems","display_name":"Numerical approximations based on sextic B-spline functions for solving fourth-order singular problems","publication_year":2022,"publication_date":"2022-02-04","ids":{"openalex":"https://openalex.org/W4210776674","doi":"https://doi.org/10.1080/00207160.2022.2037576"},"language":"en","primary_location":{"id":"doi:10.1080/00207160.2022.2037576","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207160.2022.2037576","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/A5039652067","display_name":"M. Esther Rani","orcid":null},"institutions":[{"id":"https://openalex.org/I160968435","display_name":"University of Sargodha","ror":"https://ror.org/0086rpr26","country_code":"PK","type":"education","lineage":["https://openalex.org/I160968435"]}],"countries":["PK"],"is_corresponding":false,"raw_author_name":"Mehvish Rani","raw_affiliation_strings":["Department of Mathematics, University of Sargodha, Sargodha, Pakistan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Sargodha, Sargodha, Pakistan","institution_ids":["https://openalex.org/I160968435"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5019785333","display_name":"Farah Aini Abdullah","orcid":"https://orcid.org/0000-0002-5215-9617"},"institutions":[{"id":"https://openalex.org/I139322472","display_name":"Universiti Sains Malaysia","ror":"https://ror.org/02rgb2k63","country_code":"MY","type":"education","lineage":["https://openalex.org/I139322472"]}],"countries":["MY"],"is_corresponding":false,"raw_author_name":"Farah Aini Abdullah","raw_affiliation_strings":["School of Mathematical Sciences, Universiti Sains Malaysia, Penang, Malaysia"],"raw_orcid":"https://orcid.org/0000-0002-5215-9617","affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, Universiti Sains Malaysia, Penang, Malaysia","institution_ids":["https://openalex.org/I139322472"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5096800557","display_name":"Irum Samreen","orcid":null},"institutions":[{"id":"https://openalex.org/I160968435","display_name":"University of Sargodha","ror":"https://ror.org/0086rpr26","country_code":"PK","type":"education","lineage":["https://openalex.org/I160968435"]}],"countries":["PK"],"is_corresponding":false,"raw_author_name":"Irum Samreen","raw_affiliation_strings":["Department of Mathematics, University of Sargodha, Sargodha, Pakistan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Sargodha, Sargodha, Pakistan","institution_ids":["https://openalex.org/I160968435"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5036734666","display_name":"Muhammad Abbas","orcid":"https://orcid.org/0000-0002-0491-1528"},"institutions":[{"id":"https://openalex.org/I160968435","display_name":"University of Sargodha","ror":"https://ror.org/0086rpr26","country_code":"PK","type":"education","lineage":["https://openalex.org/I160968435"]}],"countries":["PK"],"is_corresponding":true,"raw_author_name":"Muhammad Abbas","raw_affiliation_strings":["Department of Mathematics, University of Sargodha, Sargodha, Pakistan"],"raw_orcid":"https://orcid.org/0000-0002-0491-1528","affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Sargodha, Sargodha, Pakistan","institution_ids":["https://openalex.org/I160968435"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5043280787","display_name":"Abdul Majeed","orcid":"https://orcid.org/0000-0002-0316-1585"},"institutions":[{"id":"https://openalex.org/I3130814776","display_name":"University of Okara","ror":"https://ror.org/02fmg6q11","country_code":"PK","type":"education","lineage":["https://openalex.org/I3130814776"]},{"id":"https://openalex.org/I5100685","display_name":"University of Education","ror":"https://ror.org/052z7nw84","country_code":"PK","type":"education","lineage":["https://openalex.org/I5100685"]}],"countries":["PK"],"is_corresponding":false,"raw_author_name":"Abdul Majeed","raw_affiliation_strings":["Department of Mathematics, Division of Science and Technology, University of Education, Lahore, Pakistan"],"raw_orcid":"https://orcid.org/0000-0002-0316-1585","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Division of Science and Technology, University of Education, Lahore, Pakistan","institution_ids":["https://openalex.org/I5100685","https://openalex.org/I3130814776"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5043412155","display_name":"Thabet Abdeljawad","orcid":"https://orcid.org/0000-0002-8889-3768"},"institutions":[{"id":"https://openalex.org/I142024983","display_name":"Prince Sultan University","ror":"https://ror.org/053mqrf26","country_code":"SA","type":"education","lineage":["https://openalex.org/I142024983"]},{"id":"https://openalex.org/I184693016","display_name":"China Medical University","ror":"https://ror.org/00v408z34","country_code":"TW","type":"education","lineage":["https://openalex.org/I184693016"]}],"countries":["SA","TW"],"is_corresponding":true,"raw_author_name":"Thabet Abdeljawad","raw_affiliation_strings":["Department of Mathematics and Sciences, Prince Sultan University, Riyadh, Saudi Arabia","Department of Medical Research, China Medical University, Taichung, Taiwan"],"raw_orcid":"https://orcid.org/0000-0002-8889-3768","affiliations":[{"raw_affiliation_string":"Department of Mathematics and Sciences, Prince Sultan University, Riyadh, Saudi Arabia","institution_ids":["https://openalex.org/I142024983"]},{"raw_affiliation_string":"Department of Medical Research, China Medical University, Taichung, Taiwan","institution_ids":["https://openalex.org/I184693016"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5082952707","display_name":"Manar A. Alqudah","orcid":"https://orcid.org/0000-0002-9066-5334"},"institutions":[{"id":"https://openalex.org/I106778892","display_name":"Princess Nourah bint Abdulrahman University","ror":"https://ror.org/05b0cyh02","country_code":"SA","type":"education","lineage":["https://openalex.org/I106778892"]}],"countries":["SA"],"is_corresponding":false,"raw_author_name":"Manar A. Alqudah","raw_affiliation_strings":["Department of Mathematical Sciences, Faculty of Sciences, Princess Nourah Bint Abdulrahman University, Riyadh, Saudi Arabia"],"raw_orcid":"https://orcid.org/0000-0002-9066-5334","affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences, Faculty of Sciences, Princess Nourah Bint Abdulrahman University, Riyadh, Saudi Arabia","institution_ids":["https://openalex.org/I106778892"]}]}],"institutions":[],"countries_distinct_count":4,"institutions_distinct_count":7,"corresponding_author_ids":["https://openalex.org/A5036734666","https://openalex.org/A5043412155"],"corresponding_institution_ids":["https://openalex.org/I142024983","https://openalex.org/I160968435","https://openalex.org/I184693016"],"apc_list":null,"apc_paid":null,"fwci":0.548,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.57444152,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"99","issue":"10","first_page":"2139","last_page":"2158"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10288","display_name":"Fractional Differential Equations Solutions","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"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/T10288","display_name":"Fractional Differential Equations Solutions","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"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/T12727","display_name":"Differential Equations and Numerical Methods","score":0.9994999766349792,"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/T12661","display_name":"Iterative Methods for Nonlinear Equations","score":0.9988999962806702,"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":0.8366552591323853},{"id":"https://openalex.org/keywords/approximations-of-\u03c0","display_name":"Approximations of \u03c0","score":0.595940887928009},{"id":"https://openalex.org/keywords/b-spline","display_name":"B-spline","score":0.5500813126564026},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5207338333129883},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.5182773470878601},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.49524345993995667},{"id":"https://openalex.org/keywords/numerical-approximation","display_name":"Numerical approximation","score":0.44405993819236755},{"id":"https://openalex.org/keywords/spline","display_name":"Spline (mechanical)","score":0.43022099137306213},{"id":"https://openalex.org/keywords/perfect-spline","display_name":"Perfect spline","score":0.41811442375183105},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3731614947319031},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.35598498582839966},{"id":"https://openalex.org/keywords/thin-plate-spline","display_name":"Thin plate spline","score":0.22152873873710632},{"id":"https://openalex.org/keywords/spline-interpolation","display_name":"Spline interpolation","score":0.16150084137916565}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8366552591323853},{"id":"https://openalex.org/C193386753","wikidata":"https://www.wikidata.org/wiki/Q1130396","display_name":"Approximations of \u03c0","level":2,"score":0.595940887928009},{"id":"https://openalex.org/C15945459","wikidata":"https://www.wikidata.org/wiki/Q2083109","display_name":"B-spline","level":2,"score":0.5500813126564026},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5207338333129883},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.5182773470878601},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.49524345993995667},{"id":"https://openalex.org/C2986878899","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical approximation","level":3,"score":0.44405993819236755},{"id":"https://openalex.org/C10390562","wikidata":"https://www.wikidata.org/wiki/Q581809","display_name":"Spline (mechanical)","level":2,"score":0.43022099137306213},{"id":"https://openalex.org/C205224112","wikidata":"https://www.wikidata.org/wiki/Q4426180","display_name":"Perfect spline","level":5,"score":0.41811442375183105},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3731614947319031},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.35598498582839966},{"id":"https://openalex.org/C93132110","wikidata":"https://www.wikidata.org/wiki/Q7784288","display_name":"Thin plate spline","level":4,"score":0.22152873873710632},{"id":"https://openalex.org/C31447003","wikidata":"https://www.wikidata.org/wiki/Q545002","display_name":"Spline interpolation","level":3,"score":0.16150084137916565},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C205203396","wikidata":"https://www.wikidata.org/wiki/Q612143","display_name":"Bilinear interpolation","level":2,"score":0.0},{"id":"https://openalex.org/C66938386","wikidata":"https://www.wikidata.org/wiki/Q633538","display_name":"Structural engineering","level":1,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/00207160.2022.2037576","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207160.2022.2037576","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/G1154381941","display_name":null,"funder_award_id":"PNURSP2022R14","funder_id":"https://openalex.org/F4320322484","funder_display_name":"Princess Nourah Bint Abdulrahman University"}],"funders":[{"id":"https://openalex.org/F4320322484","display_name":"Princess Nourah Bint Abdulrahman University","ror":"https://ror.org/05b0cyh02"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":20,"referenced_works":["https://openalex.org/W1851611276","https://openalex.org/W1972590424","https://openalex.org/W1973676901","https://openalex.org/W1982809265","https://openalex.org/W1988973528","https://openalex.org/W1992873236","https://openalex.org/W1993142934","https://openalex.org/W1993650018","https://openalex.org/W2020122895","https://openalex.org/W2027254911","https://openalex.org/W2052240292","https://openalex.org/W2062541285","https://openalex.org/W2069280641","https://openalex.org/W2194546888","https://openalex.org/W2344420529","https://openalex.org/W2526575642","https://openalex.org/W2894097723","https://openalex.org/W2899167481","https://openalex.org/W3017070889","https://openalex.org/W3126218573"],"related_works":["https://openalex.org/W1987371472","https://openalex.org/W1979498295","https://openalex.org/W2294595241","https://openalex.org/W1633071293","https://openalex.org/W2004444928","https://openalex.org/W2021549954","https://openalex.org/W2093703039","https://openalex.org/W1983031263","https://openalex.org/W2061128313","https://openalex.org/W4210776674"],"abstract_inverted_index":{"In":[0],"this":[1],"work,":[2],"a":[3,59],"new":[4],"access":[5],"for":[6,101],"solving":[7,102],"fourth-order":[8],"singular":[9],"boundary":[10,51],"value":[11,52],"problem":[12,53],"(SBVP)":[13],"by":[14,62],"using":[15],"sextic":[16],"B-spline":[17],"is":[18,55,70,96],"presented.":[19],"The":[20,93],"SBVP":[21],"yields":[22],"in":[23],"mathematical":[24],"modelling":[25],"of":[26,67,83],"several":[27],"real-world":[28],"development":[29],"essentially":[30],"electro-hydrodynamics,":[31],"chemical":[32],"reactions,":[33],"thermal":[34],"explosions,":[35],"fluid":[36],"dynamics,":[37],"aerodynamics":[38],"and":[39,81,87,99],"atomic":[40],"nuclear":[41],"reactions.":[42],"It":[43],"must":[44],"be":[45],"indicated":[46],"that":[47],"the":[48,68,79,84,90,103],"original":[49],"non-linear":[50,104],"(BVP)":[54],"first":[56],"remodelled":[57],"into":[58],"linear":[60],"BVP":[61],"quasilinearization":[63],"technique.":[64],"Convergence":[65],"analysis":[66],"method":[69,95],"explored.":[71],"Three":[72],"trial":[73],"evidences":[74],"are":[75],"examined":[76],"to":[77,88],"determine":[78],"accuracy":[80],"suitability":[82],"described":[85],"technique":[86],"validate":[89],"analytical":[91],"results.":[92],"proposed":[94],"simple,":[97],"robust":[98],"straightforward":[100],"SBVP.":[105]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
