{"id":"https://openalex.org/W1972909974","doi":"https://doi.org/10.1155/2007/10957","title":"Solution of Cauchy-Type Singular Integral Equations of the First Kind with Zeros of Jacobi Polynomials as Interpolation Nodes","display_name":"Solution of Cauchy-Type Singular Integral Equations of the First Kind with Zeros of Jacobi Polynomials as Interpolation Nodes","publication_year":2007,"publication_date":"2007-01-01","ids":{"openalex":"https://openalex.org/W1972909974","doi":"https://doi.org/10.1155/2007/10957","mag":"1972909974"},"language":"en","primary_location":{"id":"doi:10.1155/2007/10957","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2007/10957","pdf_url":"https://downloads.hindawi.com/journals/ijmms/2007/010957.pdf","source":{"id":"https://openalex.org/S151851439","display_name":"International Journal of Mathematics and Mathematical Sciences","issn_l":"0161-1712","issn":["0161-1712","1687-0425"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Mathematics and Mathematical Sciences","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://downloads.hindawi.com/journals/ijmms/2007/010957.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5081564004","display_name":"G. E. Okecha","orcid":null},"institutions":[{"id":"https://openalex.org/I114499477","display_name":"University of Fort Hare","ror":"https://ror.org/0184vwv17","country_code":"ZA","type":"education","lineage":["https://openalex.org/I114499477"]}],"countries":["ZA"],"is_corresponding":true,"raw_author_name":"G. E. Okecha","raw_affiliation_strings":["Department of Mathematics, (Pure and Applied), University of Fort Hare, South Africa"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, (Pure and Applied), University of Fort Hare, South Africa","institution_ids":["https://openalex.org/I114499477"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5081564004"],"corresponding_institution_ids":["https://openalex.org/I114499477"],"apc_list":{"value":1025,"currency":"USD","value_usd":1025},"apc_paid":{"value":1025,"currency":"USD","value_usd":1025},"fwci":0.0,"has_fulltext":true,"cited_by_count":3,"citation_normalized_percentile":{"value":0.07986907,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":96},"biblio":{"volume":"2007","issue":null,"first_page":"1","last_page":"12"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10288","display_name":"Fractional Differential Equations Solutions","score":0.9983999729156494,"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":0.9983999729156494,"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/T11191","display_name":"Mathematical functions and polynomials","score":0.996999979019165,"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":0.9965000152587891,"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":0.918519139289856},{"id":"https://openalex.org/keywords/quadrature","display_name":"Quadrature (astronomy)","score":0.5106800198554993},{"id":"https://openalex.org/keywords/interpolation","display_name":"Interpolation (computer graphics)","score":0.5046728849411011},{"id":"https://openalex.org/keywords/algebraic-equation","display_name":"Algebraic equation","score":0.4723796844482422},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4698827564716339},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.4451844394207001},{"id":"https://openalex.org/keywords/singular-integral","display_name":"Singular integral","score":0.44043025374412537},{"id":"https://openalex.org/keywords/nystr\u00f6m-method","display_name":"Nystr\u00f6m method","score":0.41445767879486084},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.38362666964530945},{"id":"https://openalex.org/keywords/integral-equation","display_name":"Integral equation","score":0.3701953887939453},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.1883116066455841}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.918519139289856},{"id":"https://openalex.org/C62869609","wikidata":"https://www.wikidata.org/wiki/Q28137","display_name":"Quadrature (astronomy)","level":2,"score":0.5106800198554993},{"id":"https://openalex.org/C137800194","wikidata":"https://www.wikidata.org/wiki/Q11713455","display_name":"Interpolation (computer graphics)","level":3,"score":0.5046728849411011},{"id":"https://openalex.org/C23917780","wikidata":"https://www.wikidata.org/wiki/Q50698","display_name":"Algebraic equation","level":3,"score":0.4723796844482422},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4698827564716339},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.4451844394207001},{"id":"https://openalex.org/C92571104","wikidata":"https://www.wikidata.org/wiki/Q888122","display_name":"Singular integral","level":3,"score":0.44043025374412537},{"id":"https://openalex.org/C48265008","wikidata":"https://www.wikidata.org/wiki/Q7071295","display_name":"Nystr\u00f6m method","level":3,"score":0.41445767879486084},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.38362666964530945},{"id":"https://openalex.org/C27016315","wikidata":"https://www.wikidata.org/wiki/Q580101","display_name":"Integral equation","level":2,"score":0.3701953887939453},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.1883116066455841},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","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/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","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},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C119599485","wikidata":"https://www.wikidata.org/wiki/Q43035","display_name":"Electrical engineering","level":1,"score":0.0},{"id":"https://openalex.org/C121684516","wikidata":"https://www.wikidata.org/wiki/Q7600677","display_name":"Computer graphics (images)","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1155/2007/10957","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2007/10957","pdf_url":"https://downloads.hindawi.com/journals/ijmms/2007/010957.pdf","source":{"id":"https://openalex.org/S151851439","display_name":"International Journal of Mathematics and Mathematical Sciences","issn_l":"0161-1712","issn":["0161-1712","1687-0425"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Mathematics and Mathematical Sciences","raw_type":"journal-article"},{"id":"pmh:oai:RePEc:hin:jijmms:010957","is_oa":false,"landing_page_url":"http://downloads.hindawi.com/journals/IJMMS/2007/010957.xml","pdf_url":null,"source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"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":"article"},{"id":"pmh:oai:doaj.org/article:edcb168234784a41a4d2b29cfa715b62","is_oa":true,"landing_page_url":"https://doaj.org/article/edcb168234784a41a4d2b29cfa715b62","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","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":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"International Journal of Mathematics and Mathematical Sciences, Vol 2007 (2007)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1155/2007/10957","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2007/10957","pdf_url":"https://downloads.hindawi.com/journals/ijmms/2007/010957.pdf","source":{"id":"https://openalex.org/S151851439","display_name":"International Journal of Mathematics and Mathematical Sciences","issn_l":"0161-1712","issn":["0161-1712","1687-0425"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Mathematics and Mathematical Sciences","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320337380","display_name":"Division of Mathematical Sciences","ror":"https://ror.org/051fftw81"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1972909974.pdf","grobid_xml":"https://content.openalex.org/works/W1972909974.grobid-xml"},"referenced_works_count":9,"referenced_works":["https://openalex.org/W1525618410","https://openalex.org/W1566912541","https://openalex.org/W1609413062","https://openalex.org/W1986398485","https://openalex.org/W1989721420","https://openalex.org/W2035155528","https://openalex.org/W2485825958","https://openalex.org/W2801179766","https://openalex.org/W4230901691"],"related_works":["https://openalex.org/W1963845699","https://openalex.org/W1994364604","https://openalex.org/W2545824990","https://openalex.org/W2061461757","https://openalex.org/W1667827684","https://openalex.org/W2063886624","https://openalex.org/W2389601816","https://openalex.org/W2069733545","https://openalex.org/W2024862778","https://openalex.org/W2942108226"],"abstract_inverted_index":{"Of":[0],"concern":[1],"in":[2],"this":[3,93],"paper":[4],"is":[5,39,47,63,83],"the":[6,15,32,61,75,78],"numerical":[7,67],"solution":[8],"of":[9,14,22,34,52,77],"Cauchy-type":[10],"singular":[11],"integral":[12],"equations":[13],"first":[16],"kind":[17],"at":[18],"a":[19,50],"discrete":[20],"set":[21],"points.":[23],"A":[24,56,65],"quadrature":[25],"rule":[26],"based":[27],"on":[28],"Lagrangian":[29],"interpolation,":[30],"with":[31],"zeros":[33],"Jacobi":[35],"polynomials":[36],"as":[37],"nodes,":[38],"developed":[40,90],"to":[41,49,71,91],"solve":[42],"these":[43],"equations.":[44,55],"The":[45],"problem":[46],"reduced":[48],"system":[51],"linear":[53],"algebraic":[54],"theoretical":[57],"convergence":[58],"result":[59],"for":[60],"approximation":[62],"provided.":[64],"few":[66],"results":[68],"are":[69],"given":[70],"illustrate":[72],"and":[73],"validate":[74],"power":[76],"method":[79,82],"developed.":[80],"Our":[81],"more":[84],"accurate":[85],"than":[86],"some":[87],"earlier":[88],"methods":[89],"tackle":[92],"problem.":[94]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2018,"cited_by_count":2}],"updated_date":"2026-05-06T08:25:59.206177","created_date":"2025-10-10T00:00:00"}
