{"id":"https://openalex.org/W4212767907","doi":"https://doi.org/10.1080/00207160.2022.2037133","title":"Numerical solution of two-dimensional nonlinear Volterra integral equations of the first kind using operational matrices of hybrid functions","display_name":"Numerical solution of two-dimensional nonlinear Volterra integral equations of the first kind using operational matrices of hybrid functions","publication_year":2022,"publication_date":"2022-02-14","ids":{"openalex":"https://openalex.org/W4212767907","doi":"https://doi.org/10.1080/00207160.2022.2037133"},"language":"en","primary_location":{"id":"doi:10.1080/00207160.2022.2037133","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207160.2022.2037133","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/A5032667200","display_name":"K. Maleknejad","orcid":"https://orcid.org/0000-0003-1774-7525"},"institutions":[{"id":"https://openalex.org/I67009956","display_name":"Iran University of Science and Technology","ror":"https://ror.org/01jw2p796","country_code":"IR","type":"education","lineage":["https://openalex.org/I67009956"]}],"countries":["IR"],"is_corresponding":true,"raw_author_name":"K. Maleknejad","raw_affiliation_strings":["School of Mathematics, Iran University of Science & Technology, Tehran, Iran"],"affiliations":[{"raw_affiliation_string":"School of Mathematics, Iran University of Science & Technology, Tehran, Iran","institution_ids":["https://openalex.org/I67009956"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5102846062","display_name":"M. Shahabi","orcid":"https://orcid.org/0000-0002-9837-7126"},"institutions":[{"id":"https://openalex.org/I67009956","display_name":"Iran University of Science and Technology","ror":"https://ror.org/01jw2p796","country_code":"IR","type":"education","lineage":["https://openalex.org/I67009956"]}],"countries":["IR"],"is_corresponding":false,"raw_author_name":"M. Shahabi","raw_affiliation_strings":["School of Mathematics, Iran University of Science & Technology, Tehran, Iran"],"affiliations":[{"raw_affiliation_string":"School of Mathematics, Iran University of Science & Technology, Tehran, Iran","institution_ids":["https://openalex.org/I67009956"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5032667200"],"corresponding_institution_ids":["https://openalex.org/I67009956"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.01294086,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"99","issue":"10","first_page":"2105","last_page":"2122"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"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"}},"topics":[{"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/T12727","display_name":"Differential Equations and Numerical Methods","score":0.995199978351593,"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/T10739","display_name":"Electromagnetic Scattering and Analysis","score":0.9882000088691711,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8066535592079163},{"id":"https://openalex.org/keywords/volterra-integral-equation","display_name":"Volterra integral equation","score":0.7787235975265503},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5965830087661743},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.5641364455223083},{"id":"https://openalex.org/keywords/integral-equation","display_name":"Integral equation","score":0.515108048915863},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5068939328193665},{"id":"https://openalex.org/keywords/volterra-equations","display_name":"Volterra equations","score":0.45761576294898987},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4265672266483307}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8066535592079163},{"id":"https://openalex.org/C21965488","wikidata":"https://www.wikidata.org/wiki/Q2632613","display_name":"Volterra integral equation","level":3,"score":0.7787235975265503},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5965830087661743},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.5641364455223083},{"id":"https://openalex.org/C27016315","wikidata":"https://www.wikidata.org/wiki/Q580101","display_name":"Integral equation","level":2,"score":0.515108048915863},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5068939328193665},{"id":"https://openalex.org/C2983756050","wikidata":"https://www.wikidata.org/wiki/Q150052","display_name":"Volterra equations","level":3,"score":0.45761576294898987},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4265672266483307},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/00207160.2022.2037133","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207160.2022.2037133","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":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":29,"referenced_works":["https://openalex.org/W1555494686","https://openalex.org/W1567668233","https://openalex.org/W1582171922","https://openalex.org/W1969428492","https://openalex.org/W1971554778","https://openalex.org/W1974260053","https://openalex.org/W2007751765","https://openalex.org/W2009966622","https://openalex.org/W2026762845","https://openalex.org/W2064972606","https://openalex.org/W2068761599","https://openalex.org/W2085063499","https://openalex.org/W2092946348","https://openalex.org/W2107221565","https://openalex.org/W2113455343","https://openalex.org/W2156561450","https://openalex.org/W2513196354","https://openalex.org/W2603722043","https://openalex.org/W2894195044","https://openalex.org/W2955944315","https://openalex.org/W2975138513","https://openalex.org/W2982644695","https://openalex.org/W2986132802","https://openalex.org/W3004706596","https://openalex.org/W3009194266","https://openalex.org/W3013883941","https://openalex.org/W3042729733","https://openalex.org/W3095594153","https://openalex.org/W3133596807"],"related_works":["https://openalex.org/W2087114507","https://openalex.org/W2145565532","https://openalex.org/W2782544673","https://openalex.org/W2534348686","https://openalex.org/W1826865795","https://openalex.org/W4319926487","https://openalex.org/W2045354458","https://openalex.org/W1965500773","https://openalex.org/W4236115800","https://openalex.org/W2165778807"],"abstract_inverted_index":{"In":[0],"this":[1,32],"paper,":[2],"operational":[3,52,60],"matrices":[4,53],"of":[5,8,20,26,45,54,72,77,104],"two-dimensional":[6,21,40],"hybrid":[7],"block-pulse":[9],"functions":[10,112],"and":[11,83,102],"Legendre":[12],"polynomials":[13],"are":[14,96,114],"employed":[15],"to":[16,38,65,69,98],"approximate":[17],"the":[18,27,39,46,51,58,67,78,88,100,105,118],"solutions":[19],"nonlinear":[22],"Volterra":[23,42],"integral":[24,43],"equations":[25,44],"first":[28,35],"kind":[29,48],"(2DNVIEF).":[30],"To":[31],"aim,":[33],"we":[34],"convert":[36],"2DNVIEF":[37],"linear":[41],"second":[47],"(2DLVIES).":[49],"Then":[50],"integration,":[55],"together":[56],"with":[57,111],"product":[59],"matrix,":[61],"can":[62],"be":[63],"applied":[64],"reduce":[66],"2DLVIES":[68],"a":[70],"system":[71],"algebraic":[73],"equations.":[74],"The":[75],"convergence":[76],"proposed":[79],"method":[80,107],"is":[81,90],"studied,":[82],"an":[84],"error":[85],"estimation":[86],"under":[87],"L2-norm":[89],"provided.":[91],"Finally,":[92],"some":[93],"numerical":[94,106],"examples":[95],"prepared":[97],"clarify":[99],"accuracy":[101],"efficiency":[103],"especially":[108],"in":[109,117],"dealing":[110],"that":[113],"not":[115],"continuous":[116],"whole":[119],"interval.":[120]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}