{"id":"https://openalex.org/W2155420055","doi":"https://doi.org/10.2478/amcs-2013-0026","title":"Convergence analysis of piecewise continuous collocation methods for higher index integral algebraic equations of the Hessenberg type","display_name":"Convergence analysis of piecewise continuous collocation methods for higher index integral algebraic equations of the Hessenberg type","publication_year":2013,"publication_date":"2013-06-01","ids":{"openalex":"https://openalex.org/W2155420055","doi":"https://doi.org/10.2478/amcs-2013-0026","mag":"2155420055"},"language":"en","primary_location":{"id":"doi:10.2478/amcs-2013-0026","is_oa":true,"landing_page_url":"https://doi.org/10.2478/amcs-2013-0026","pdf_url":"https://sciendo.com/pdf/10.2478/amcs-2013-0026","source":{"id":"https://openalex.org/S117679522","display_name":"International Journal of Applied Mathematics and Computer Science","issn_l":"1641-876X","issn":["1641-876X","2083-8492"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310320322","host_organization_name":"De Gruyter Open","host_organization_lineage":["https://openalex.org/P4310320322","https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter Open","De Gruyter"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Applied Mathematics and Computer Science","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://sciendo.com/pdf/10.2478/amcs-2013-0026","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5041380674","display_name":"Babak Shiri","orcid":"https://orcid.org/0000-0003-2249-282X"},"institutions":[{"id":"https://openalex.org/I41832843","display_name":"University of Tabriz","ror":"https://ror.org/01papkj44","country_code":"IR","type":"education","lineage":["https://openalex.org/I41832843"]}],"countries":["IR"],"is_corresponding":true,"raw_author_name":"Babak Shiri","raw_affiliation_strings":["Faculty of Mathematical Sciences University of Tabriz, 29 Bahmn Boulevard, 5166616471 Tabriz, Iran"],"affiliations":[{"raw_affiliation_string":"Faculty of Mathematical Sciences University of Tabriz, 29 Bahmn Boulevard, 5166616471 Tabriz, Iran","institution_ids":["https://openalex.org/I41832843"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5070053895","display_name":"S. Shahmorad","orcid":"https://orcid.org/0000-0002-2476-1176"},"institutions":[{"id":"https://openalex.org/I41832843","display_name":"University of Tabriz","ror":"https://ror.org/01papkj44","country_code":"IR","type":"education","lineage":["https://openalex.org/I41832843"]}],"countries":["IR"],"is_corresponding":false,"raw_author_name":"Sedaghat Shahmorad","raw_affiliation_strings":["Faculty of Mathematical Sciences University of Tabriz, 29 Bahmn Boulevard, 5166616471 Tabriz, Iran"],"affiliations":[{"raw_affiliation_string":"Faculty of Mathematical Sciences University of Tabriz, 29 Bahmn Boulevard, 5166616471 Tabriz, Iran","institution_ids":["https://openalex.org/I41832843"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5080290364","display_name":"Gholamreza Hojjati","orcid":"https://orcid.org/0000-0001-8406-763X"},"institutions":[{"id":"https://openalex.org/I41832843","display_name":"University of Tabriz","ror":"https://ror.org/01papkj44","country_code":"IR","type":"education","lineage":["https://openalex.org/I41832843"]}],"countries":["IR"],"is_corresponding":false,"raw_author_name":"Gholamreza Hojjati","raw_affiliation_strings":["Faculty of Mathematical Sciences University of Tabriz, 29 Bahmn Boulevard, 5166616471 Tabriz, Iran"],"affiliations":[{"raw_affiliation_string":"Faculty of Mathematical Sciences University of Tabriz, 29 Bahmn Boulevard, 5166616471 Tabriz, Iran","institution_ids":["https://openalex.org/I41832843"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5041380674"],"corresponding_institution_ids":["https://openalex.org/I41832843"],"apc_list":{"value":4080,"currency":"PLN","value_usd":1100},"apc_paid":{"value":4080,"currency":"PLN","value_usd":1100},"fwci":2.777,"has_fulltext":true,"cited_by_count":18,"citation_normalized_percentile":{"value":0.90333264,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"23","issue":"2","first_page":"341","last_page":"355"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12727","display_name":"Differential Equations and Numerical Methods","score":0.9995999932289124,"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":0.9995999932289124,"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/T10288","display_name":"Fractional Differential Equations Solutions","score":0.9987999796867371,"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/T12661","display_name":"Iterative Methods for Nonlinear Equations","score":0.993399977684021,"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/piecewise","display_name":"Piecewise","score":0.8005555868148804},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7774549722671509},{"id":"https://openalex.org/keywords/collocation","display_name":"Collocation (remote sensing)","score":0.7130559086799622},{"id":"https://openalex.org/keywords/collocation-method","display_name":"Collocation method","score":0.6610041260719299},{"id":"https://openalex.org/keywords/algebraic-equation","display_name":"Algebraic equation","score":0.6250074505805969},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5892003178596497},{"id":"https://openalex.org/keywords/uniqueness","display_name":"Uniqueness","score":0.5687723159790039},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5072614550590515},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.44451650977134705},{"id":"https://openalex.org/keywords/orthogonal-collocation","display_name":"Orthogonal collocation","score":0.43922606110572815},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.43487095832824707},{"id":"https://openalex.org/keywords/integral-equation","display_name":"Integral equation","score":0.42582231760025024},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.42265915870666504},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3706742227077484},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.13219672441482544},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.1200098991394043},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.11212071776390076},{"id":"https://openalex.org/keywords/ordinary-differential-equation","display_name":"Ordinary differential equation","score":0.07308840751647949}],"concepts":[{"id":"https://openalex.org/C164660894","wikidata":"https://www.wikidata.org/wiki/Q2037833","display_name":"Piecewise","level":2,"score":0.8005555868148804},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7774549722671509},{"id":"https://openalex.org/C80023036","wikidata":"https://www.wikidata.org/wiki/Q5147531","display_name":"Collocation (remote sensing)","level":2,"score":0.7130559086799622},{"id":"https://openalex.org/C2126413","wikidata":"https://www.wikidata.org/wiki/Q1779479","display_name":"Collocation method","level":4,"score":0.6610041260719299},{"id":"https://openalex.org/C23917780","wikidata":"https://www.wikidata.org/wiki/Q50698","display_name":"Algebraic equation","level":3,"score":0.6250074505805969},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5892003178596497},{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.5687723159790039},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5072614550590515},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.44451650977134705},{"id":"https://openalex.org/C114609681","wikidata":"https://www.wikidata.org/wiki/Q24839227","display_name":"Orthogonal collocation","level":5,"score":0.43922606110572815},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.43487095832824707},{"id":"https://openalex.org/C27016315","wikidata":"https://www.wikidata.org/wiki/Q580101","display_name":"Integral equation","level":2,"score":0.42582231760025024},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.42265915870666504},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3706742227077484},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.13219672441482544},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.1200098991394043},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.11212071776390076},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.07308840751647949},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"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/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"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/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.2478/amcs-2013-0026","is_oa":true,"landing_page_url":"https://doi.org/10.2478/amcs-2013-0026","pdf_url":"https://sciendo.com/pdf/10.2478/amcs-2013-0026","source":{"id":"https://openalex.org/S117679522","display_name":"International Journal of Applied Mathematics and Computer Science","issn_l":"1641-876X","issn":["1641-876X","2083-8492"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310320322","host_organization_name":"De Gruyter Open","host_organization_lineage":["https://openalex.org/P4310320322","https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter Open","De Gruyter"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Applied Mathematics and Computer Science","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.2478/amcs-2013-0026","is_oa":true,"landing_page_url":"https://doi.org/10.2478/amcs-2013-0026","pdf_url":"https://sciendo.com/pdf/10.2478/amcs-2013-0026","source":{"id":"https://openalex.org/S117679522","display_name":"International Journal of Applied Mathematics and Computer Science","issn_l":"1641-876X","issn":["1641-876X","2083-8492"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310320322","host_organization_name":"De Gruyter Open","host_organization_lineage":["https://openalex.org/P4310320322","https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter Open","De Gruyter"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Applied Mathematics and Computer Science","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2155420055.pdf","grobid_xml":"https://content.openalex.org/works/W2155420055.grobid-xml"},"referenced_works_count":18,"referenced_works":["https://openalex.org/W191236717","https://openalex.org/W1543326485","https://openalex.org/W1971727543","https://openalex.org/W1973237280","https://openalex.org/W1980271875","https://openalex.org/W1984189962","https://openalex.org/W2005681763","https://openalex.org/W2053759540","https://openalex.org/W2066943818","https://openalex.org/W2075518743","https://openalex.org/W2078862466","https://openalex.org/W2081398364","https://openalex.org/W2088977327","https://openalex.org/W2104427203","https://openalex.org/W2104896764","https://openalex.org/W2320758560","https://openalex.org/W4240938322","https://openalex.org/W4243860376"],"related_works":["https://openalex.org/W2791210196","https://openalex.org/W4255016916","https://openalex.org/W2078318892","https://openalex.org/W2111003632","https://openalex.org/W2889856026","https://openalex.org/W1987365920","https://openalex.org/W1989122168","https://openalex.org/W2000247808","https://openalex.org/W2384941625","https://openalex.org/W2060099884"],"abstract_inverted_index":{"In":[0],"this":[1,29,43],"paper,":[2],"we":[3],"deal":[4],"with":[5],"a":[6,17,26],"system":[7,30,44],"of":[8,12,25,50,63],"integral":[9],"algebraic":[10],"equations":[11],"the":[13,21,47,51,61,66,78],"Hessenberg":[14],"type.":[15],"Using":[16],"new":[18],"index":[19],"definition,":[20],"existence":[22],"and":[23,46],"uniqueness":[24],"solution":[27],"to":[28,41,59,76],"are":[31,39,57,74],"studied.":[32],"The":[33],"well-known":[34],"piecewise":[35,53],"continuous":[36,54],"collocation":[37,55],"methods":[38,56],"used":[40],"solve":[42],"numerically,":[45],"convergence":[48,64],"properties":[49],"perturbed":[52],"investigated":[58],"obtain":[60],"order":[62],"for":[65],"given":[67],"numerical":[68,72],"methods.":[69],"Finally,":[70],"some":[71],"experiments":[73],"provided":[75],"support":[77],"theoretical":[79],"results.":[80]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":3},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":1},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":1},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}