{"id":"https://openalex.org/W4390744679","doi":"https://doi.org/10.1108/hff-09-2023-0553","title":"Precision and efficiency of an interpolation approach to weakly singular integral equations","display_name":"Precision and efficiency of an interpolation approach to weakly singular integral equations","publication_year":2024,"publication_date":"2024-01-11","ids":{"openalex":"https://openalex.org/W4390744679","doi":"https://doi.org/10.1108/hff-09-2023-0553"},"language":"en","primary_location":{"id":"doi:10.1108/hff-09-2023-0553","doi":"https://doi.org/10.1108/hff-09-2023-0553","is_oa":false,"landing_page_url":"https://doi.org/10.1108/hff-09-2023-0553","pdf_url":null,"source":{"id":"https://openalex.org/S116405997","display_name":"International Journal of Numerical Methods for Heat &amp Fluid Flow","issn_l":"0961-5539","issn":["0961-5539","1758-6585"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","dongbi-b","jufo-1","norway-1","poland-100","russia-white-list-1"],"host_organization":"https://openalex.org/P4310319811","host_organization_name":"Emerald Publishing Limited","host_organization_lineage":["https://openalex.org/P4310319811"],"host_organization_lineage_names":["Emerald Publishing Limited"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Numerical Methods for Heat & Fluid Flow","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"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/A5101915405","display_name":"Imtiyaz Ahmad Bhat","orcid":"https://orcid.org/0000-0002-6852-9619","observed_orcids":["https://orcid.org/0000-0002-6852-9619"]},"institutions":[{"id":"https://openalex.org/I876193797","display_name":"Vellore Institute of Technology University","ror":"https://ror.org/00qzypv28","country_code":"IN","type":"education","lineage":["https://openalex.org/I876193797"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Imtiyaz Ahmad Bhat","raw_affiliation_strings":["Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Vellore, India"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Vellore, India","institution_ids":["https://openalex.org/I876193797"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5054777936","display_name":"Lakshmi Narayan Mishra","orcid":"https://orcid.org/0000-0001-7774-7290","observed_orcids":["https://orcid.org/0000-0001-7774-7290"]},"institutions":[{"id":"https://openalex.org/I876193797","display_name":"Vellore Institute of Technology University","ror":"https://ror.org/00qzypv28","country_code":"IN","type":"education","lineage":["https://openalex.org/I876193797"]}],"countries":["IN"],"is_corresponding":true,"raw_author_name":"Lakshmi Narayan Mishra","raw_affiliation_strings":["Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Vellore, India"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Vellore, India","institution_ids":["https://openalex.org/I876193797"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5009385455","display_name":"Vishnu Narayan Mishra","orcid":"https://orcid.org/0000-0002-2159-7710","observed_orcids":["https://orcid.org/0000-0002-2159-7710"]},"institutions":[{"id":"https://openalex.org/I296362101","display_name":"Indira Gandhi National Tribal University","ror":"https://ror.org/04yayy336","country_code":"IN","type":"education","lineage":["https://openalex.org/I296362101"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Vishnu Narayan Mishra","raw_affiliation_strings":["Department of Mathematics, Indira Gandhi National Tribal University, Amarkantak, India"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Indira Gandhi National Tribal University, Amarkantak, India","institution_ids":["https://openalex.org/I296362101"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5054651401","display_name":"Cemil Tun\u00e7","orcid":"https://orcid.org/0000-0003-2909-8753","observed_orcids":["https://orcid.org/0000-0003-2909-8753"]},"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":"Cemil Tun\u00e7","raw_affiliation_strings":["Department of Mathematics, Faculty of Sciences, Van Yuzuncu Yil University, Van, Turkey"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Faculty of Sciences, Van Yuzuncu Yil University, Van, Turkey","institution_ids":["https://openalex.org/I118567650"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5085174760","display_name":"Osman Tun\u00e7","orcid":"https://orcid.org/0000-0003-2965-4561","observed_orcids":["https://orcid.org/0000-0003-2965-4561"]},"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":"Osman Tun\u00e7","raw_affiliation_strings":["Department of Computer Programing, Baskale Vocational School, Van Yuzuncu Yil University, Van, Turkey"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Programing, Baskale Vocational School, Van Yuzuncu Yil University, Van, Turkey","institution_ids":["https://openalex.org/I118567650"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5054777936"],"corresponding_institution_ids":["https://openalex.org/I876193797"],"apc_list":null,"apc_paid":null,"fwci":10.2258,"has_fulltext":false,"cited_by_count":32,"citation_normalized_percentile":{"value":0.99504067,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":97,"max":99},"biblio":{"volume":"34","issue":"3","first_page":"1479","last_page":"1499"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12589","display_name":"Differential Equations and Boundary Problems","score":0.8812999725341797,"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"}},"topics":[{"id":"https://openalex.org/T12589","display_name":"Differential Equations and Boundary Problems","score":0.8812999725341797,"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/T11191","display_name":"Mathematical functions and polynomials","score":0.05510000139474869,"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/T12661","display_name":"Iterative Methods for Nonlinear Equations","score":0.013100000098347664,"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/weakly-singular-integral-equations","display_name":"weakly singular integral equations","score":0.996999979019165},{"id":"https://openalex.org/keywords/volterra-integral-equations","display_name":"Volterra integral equations","score":0.9559999704360962},{"id":"https://openalex.org/keywords/fredholm-integral-equations","display_name":"Fredholm integral equations","score":0.9919999837875366},{"id":"https://openalex.org/keywords/bicgstab","display_name":"BiCGSTAB","score":0.8999999761581421},{"id":"https://openalex.org/keywords/banach-fixed-point-theorem","display_name":"Banach fixed point theorem","score":0.8389999866485596},{"id":"https://openalex.org/keywords/existence-and-uniqueness-of-solutions","display_name":"existence and uniqueness of solutions","score":0.921999990940094},{"id":"https://openalex.org/keywords/convergence-analysis","display_name":"convergence analysis","score":0.9729999899864197},{"id":"https://openalex.org/keywords/error-estimation","display_name":"error estimation","score":0.9959999918937683},{"id":"https://openalex.org/keywords/non-smooth-kernels","display_name":"non-smooth kernels","score":0.8270000219345093},{"id":"https://openalex.org/keywords/heat-conduction","display_name":"heat conduction","score":0.9359999895095825},{"id":"https://openalex.org/keywords/systems-of-algebraic-equations","display_name":"systems of algebraic equations","score":0.5989999771118164},{"id":"https://openalex.org/keywords/numerical-solution-of-integral-equations","display_name":"numerical solution of integral equations","score":0.6759999990463257}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6894423961639404},{"id":"https://openalex.org/C27016315","wikidata":"https://www.wikidata.org/wiki/Q580101","display_name":"Integral equation","level":2,"score":0.6699886322021484},{"id":"https://openalex.org/C21965488","wikidata":"https://www.wikidata.org/wiki/Q2632613","display_name":"Volterra integral equation","level":3,"score":0.5528044700622559},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.498737096786499},{"id":"https://openalex.org/C137800194","wikidata":"https://www.wikidata.org/wiki/Q11713455","display_name":"Interpolation (computer graphics)","level":3,"score":0.4749605655670166},{"id":"https://openalex.org/C92571104","wikidata":"https://www.wikidata.org/wiki/Q888122","display_name":"Singular integral","level":3,"score":0.4662216007709503},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.45424067974090576},{"id":"https://openalex.org/C64208722","wikidata":"https://www.wikidata.org/wiki/Q861606","display_name":"Lagrange polynomial","level":3,"score":0.43453627824783325},{"id":"https://openalex.org/C23917780","wikidata":"https://www.wikidata.org/wiki/Q50698","display_name":"Algebraic equation","level":3,"score":0.4276522994041443},{"id":"https://openalex.org/C89285879","wikidata":"https://www.wikidata.org/wiki/Q2991898","display_name":"Fredholm integral equation","level":3,"score":0.4110896587371826},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.38094019889831543},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.24499258399009705},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.14314624667167664},{"id":"https://openalex.org/C121684516","wikidata":"https://www.wikidata.org/wiki/Q7600677","display_name":"Computer graphics (images)","level":1,"score":0.0},{"id":"https://openalex.org/C502989409","wikidata":"https://www.wikidata.org/wiki/Q11425","display_name":"Animation","level":2,"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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1108/hff-09-2023-0553","doi":"https://doi.org/10.1108/hff-09-2023-0553","is_oa":false,"landing_page_url":"https://doi.org/10.1108/hff-09-2023-0553","pdf_url":null,"source":{"id":"https://openalex.org/S116405997","display_name":"International Journal of Numerical Methods for Heat &amp Fluid Flow","issn_l":"0961-5539","issn":["0961-5539","1758-6585"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","dongbi-b","jufo-1","norway-1","poland-100","russia-white-list-1"],"host_organization":"https://openalex.org/P4310319811","host_organization_name":"Emerald Publishing Limited","host_organization_lineage":["https://openalex.org/P4310319811"],"host_organization_lineage_names":["Emerald Publishing Limited"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Numerical Methods for Heat & Fluid Flow","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":39,"referenced_works":["https://openalex.org/W1975325626","https://openalex.org/W2054016546","https://openalex.org/W2074742486","https://openalex.org/W2139740525","https://openalex.org/W2290568416","https://openalex.org/W2338392580","https://openalex.org/W2571827303","https://openalex.org/W2887561794","https://openalex.org/W2892499418","https://openalex.org/W2938553396","https://openalex.org/W3001806235","https://openalex.org/W3006180344","https://openalex.org/W3008016780","https://openalex.org/W3028167646","https://openalex.org/W3081918956","https://openalex.org/W3131721887","https://openalex.org/W3135526639","https://openalex.org/W3162196362","https://openalex.org/W3174926459","https://openalex.org/W3193794060","https://openalex.org/W3196127683","https://openalex.org/W4210399339","https://openalex.org/W4214874637","https://openalex.org/W4224095894","https://openalex.org/W4226030311","https://openalex.org/W4246307558","https://openalex.org/W4253740803","https://openalex.org/W4285009971","https://openalex.org/W4285040654","https://openalex.org/W4288085597","https://openalex.org/W4294152644","https://openalex.org/W4307684799","https://openalex.org/W4309001855","https://openalex.org/W4311955453","https://openalex.org/W4313411151","https://openalex.org/W4367680121","https://openalex.org/W4377293781","https://openalex.org/W4382876994","https://openalex.org/W4387710915"],"related_works":["https://openalex.org/W3174926459","https://openalex.org/W4226030311","https://openalex.org/W4214874637","https://openalex.org/W3148015573","https://openalex.org/W2793369813","https://openalex.org/W3161316854","https://openalex.org/W2594500805","https://openalex.org/W7171645547","https://openalex.org/W4289517085","https://openalex.org/W1986695776"],"abstract_inverted_index":{"Purpose":[0],"This":[1,359],"study":[2],"aims":[3],"to":[4,20,85,149,159,189,206,235,276,293,335,347,379,437],"discuss":[5],"the":[6,22,30,35,43,52,55,59,65,68,80,87,91,104,107,111,132,135,150,156,160,168,174,191,199,207,227,230,237,268,280,316,348,381,384,388,391,394,397,418,422,427,431,443],"numerical":[7,88,143,305],"solutions":[8,57,89],"of":[9,54,58,67,90,94,106,118,134,155,164,178,221,229,250,310,323,326,375,377,383,390,401,430],"weakly":[10,95,165,179,367,410],"singular":[11,96,166,180,368,411],"Volterra":[12,97,175,412],"and":[13,29,72,98,137,153,185,194,239,274,282,333,350,354,399,413,425],"Fredholm":[14,99,161,414],"integral":[15,60,100,162,176,248,369,415],"equations,":[16],"which":[17,147,196],"are":[18,140,145,187,289,315],"used":[19,319],"model":[21],"problems":[23],"like":[24,352],"heat":[25],"conduction":[26],"in":[27,64,204,243,264,408,442],"engineering":[28],"electrostatic":[31],"potential":[32],"theory,":[33],"using":[34,110],"modified":[36,81],"Lagrange":[37,82],"polynomial":[38,83],"interpolation":[39,105],"technique":[40,170],"combined":[41],"with":[42],"biconjugate":[44],"gradient":[45],"stabilized":[46],"method":[47,84,113,136,201,364],"(BiCGSTAB).":[48],"The":[49,76,210,219],"framework":[50],"for":[51,173,302,307,344,365,417],"existence":[53],"unique":[56],"equations":[61,119,163,177,249,370,416],"is":[62,121,224,233,272,298],"provided":[63,146,188],"context":[66],"Banach":[69],"contraction":[70],"principle":[71],"Bielecki":[73],"norm.":[74],"Design/methodology/approach":[75],"authors":[77,395],"have":[78],"applied":[79],"approximate":[86,240],"second":[92],"kind":[93],"equations.":[101,311],"Findings":[102],"Approaching":[103],"unknown":[108],"function":[109],"aforementioned":[112],"generates":[114],"an":[115,124],"algebraic":[116],"system":[117,271],"that":[120,198],"solved":[122],"by":[123,214,247,440],"appropriate":[125],"classical":[126],"technique.":[127],"Furthermore,":[128,182],"some":[129],"theorems":[130],"concerning":[131],"convergence":[133,220,281],"error":[138,284],"estimation":[139],"proved.":[141],"Some":[142],"examples":[144,184],"attest":[148],"application,":[151],"effectiveness":[152,400],"reliability":[154],"method.":[157,209],"Compared":[158],"type,":[167],"current":[169],"works":[171,202],"better":[172],"type.":[181],"illustrative":[183],"comparisons":[186],"show":[190],"approach\u2019s":[192],"validity":[193],"practicality,":[195],"demonstrates":[197],"present":[200],"well":[203,263],"contrast":[205],"referenced":[208],"computations":[211],"were":[212],"performed":[213],"MATLAB":[215],"software.":[216],"Research":[217],"limitations/implications":[218],"these":[222,265,308],"methods":[223],"dependent":[225],"on":[226,330],"smoothness":[228],"solution,":[231,432],"it":[232,241],"challenging":[234],"find":[236],"solution":[238],"computationally":[242],"various":[244],"applications":[245],"modelled":[246],"non-smooth":[251],"kernels.":[252],"Traditional":[253],"analytical":[254],"techniques,":[255],"such":[256],"as":[257],"projection":[258],"methods,":[259],"do":[260],"not":[261],"work":[262,360],"cases":[266],"since":[267],"produced":[269],"linear":[270],"unconditioned":[273],"hard":[275],"address.":[277],"Also,":[278],"proving":[279],"estimating":[283],"might":[285],"be":[286,438],"difficult.":[287],"They":[288],"frequently":[290,318],"also":[291],"expensive":[292],"implement.":[294],"Practical":[295],"implications":[296,358],"There":[297],"a":[299,338,362,433],"great":[300],"need":[301],"fast,":[303],"user-friendly":[304],"techniques":[306],"types":[309],"In":[312],"addition,":[313],"polynomials":[314],"most":[317],"mathematical":[320],"tools":[321],"because":[322],"their":[324,402],"ease":[325],"expression,":[327],"quick":[328],"computation":[329],"modern":[331],"computers":[332],"simple":[334],"define.":[336],"As":[337],"result,":[339],"they":[340],"made":[341],"substantial":[342],"contributions":[343],"many":[345],"years":[346],"theories":[349],"analysis":[351],"approximation":[353],"numerical,":[355],"respectively.":[356],"Social":[357],"presents":[361],"useful":[363],"handling":[366],"without":[371],"involving":[372],"any":[373],"process":[374],"change":[376],"variables":[378],"eliminate":[380],"singularity":[382,429],"solution.":[385],"Originality/value":[386],"To":[387],"best":[389],"authors\u2019":[392],"knowledge,":[393],"claim":[396],"originality":[398],"work,":[403],"highlighting":[404],"its":[405],"successful":[406],"application":[407],"addressing":[409],"first":[419],"time.":[420],"Importantly,":[421],"approach":[423],"acknowledges":[424],"preserves":[426],"possible":[428],"novel":[434],"aspect":[435],"yet":[436],"explored":[439],"researchers":[441],"field.":[444]},"counts_by_year":[{"year":2026,"cited_by_count":4},{"year":2025,"cited_by_count":15},{"year":2024,"cited_by_count":13}],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2024-01-13T00:00:00"}