{"id":"https://openalex.org/W3200157563","doi":"https://doi.org/10.1007/s40314-021-01471-0","title":"Numerical simulation of Volterra\u2013Fredholm integral equations using least squares support vector regression","display_name":"Numerical simulation of Volterra\u2013Fredholm integral equations using least squares support vector regression","publication_year":2021,"publication_date":"2021-09-20","ids":{"openalex":"https://openalex.org/W3200157563","doi":"https://doi.org/10.1007/s40314-021-01471-0","mag":"3200157563"},"language":"en","primary_location":{"id":"doi:10.1007/s40314-021-01471-0","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s40314-021-01471-0","pdf_url":null,"source":{"id":"https://openalex.org/S4210195884","display_name":"Computational and Applied Mathematics","issn_l":"1807-0302","issn":["1807-0302","2238-3603"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computational and Applied 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/A5090033177","display_name":"Kourosh Parand","orcid":"https://orcid.org/0000-0001-5946-0771"},"institutions":[{"id":"https://openalex.org/I151746483","display_name":"University of Waterloo","ror":"https://ror.org/01aff2v68","country_code":"CA","type":"education","lineage":["https://openalex.org/I151746483"]},{"id":"https://openalex.org/I3145578848","display_name":"Institute for Cognitive Science Studies","ror":"https://ror.org/0378cd528","country_code":"IR","type":"facility","lineage":["https://openalex.org/I3145578848"]},{"id":"https://openalex.org/I4210146419","display_name":"Institute for Research in Fundamental Sciences","ror":"https://ror.org/04xreqs31","country_code":"IR","type":"facility","lineage":["https://openalex.org/I4210146419"]},{"id":"https://openalex.org/I48379061","display_name":"Shahid Beheshti University","ror":"https://ror.org/0091vmj44","country_code":"IR","type":"education","lineage":["https://openalex.org/I48379061"]}],"countries":["CA","IR"],"is_corresponding":true,"raw_author_name":"K. Parand","raw_affiliation_strings":["Department of Cognitive Modeling, Institute for Cognitive and Brain Sciences, Shahid Beheshti University, G.C., Tehran, Iran","Department of Computer Sciences, Faculty of Mathematical Sciences, Shahid Beheshti University, G.C., Tehran, Iran","Department of Statistics and Actuarial Science, University of Waterloo, Waterloo, Canada","School of Computer Science, Institute for Research in Fundamental Sciences (IPM), Tehran, Iran"],"raw_orcid":"https://orcid.org/0000-0001-5946-0771","affiliations":[{"raw_affiliation_string":"Department of Cognitive Modeling, Institute for Cognitive and Brain Sciences, Shahid Beheshti University, G.C., Tehran, Iran","institution_ids":["https://openalex.org/I3145578848","https://openalex.org/I48379061"]},{"raw_affiliation_string":"Department of Computer Sciences, Faculty of Mathematical Sciences, Shahid Beheshti University, G.C., Tehran, Iran","institution_ids":["https://openalex.org/I48379061"]},{"raw_affiliation_string":"Department of Statistics and Actuarial Science, University of Waterloo, Waterloo, Canada","institution_ids":["https://openalex.org/I151746483"]},{"raw_affiliation_string":"School of Computer Science, Institute for Research in Fundamental Sciences (IPM), Tehran, Iran","institution_ids":["https://openalex.org/I4210146419"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5005138752","display_name":"Mohsen Hasani","orcid":null},"institutions":[{"id":"https://openalex.org/I48379061","display_name":"Shahid Beheshti University","ror":"https://ror.org/0091vmj44","country_code":"IR","type":"education","lineage":["https://openalex.org/I48379061"]}],"countries":["IR"],"is_corresponding":false,"raw_author_name":"M. Hasani","raw_affiliation_strings":["Department of Computer Sciences, Faculty of Mathematical Sciences, Shahid Beheshti University, G.C., Tehran, Iran"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Sciences, Faculty of Mathematical Sciences, Shahid Beheshti University, G.C., Tehran, Iran","institution_ids":["https://openalex.org/I48379061"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5030303418","display_name":"M. Jani","orcid":"https://orcid.org/0000-0002-4596-2495"},"institutions":[{"id":"https://openalex.org/I48379061","display_name":"Shahid Beheshti University","ror":"https://ror.org/0091vmj44","country_code":"IR","type":"education","lineage":["https://openalex.org/I48379061"]}],"countries":["IR"],"is_corresponding":false,"raw_author_name":"M. Jani","raw_affiliation_strings":["Department of Computer Sciences, Faculty of Mathematical Sciences, Shahid Beheshti University, G.C., Tehran, Iran"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Sciences, Faculty of Mathematical Sciences, Shahid Beheshti University, G.C., Tehran, Iran","institution_ids":["https://openalex.org/I48379061"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5082341303","display_name":"Hafez Yari","orcid":null},"institutions":[{"id":"https://openalex.org/I48379061","display_name":"Shahid Beheshti University","ror":"https://ror.org/0091vmj44","country_code":"IR","type":"education","lineage":["https://openalex.org/I48379061"]}],"countries":["IR"],"is_corresponding":false,"raw_author_name":"H. Yari","raw_affiliation_strings":["Department of Computer Sciences, Faculty of Mathematical Sciences, Shahid Beheshti University, G.C., Tehran, Iran"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Sciences, Faculty of Mathematical Sciences, Shahid Beheshti University, G.C., Tehran, Iran","institution_ids":["https://openalex.org/I48379061"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5090033177"],"corresponding_institution_ids":["https://openalex.org/I151746483","https://openalex.org/I3145578848","https://openalex.org/I4210146419","https://openalex.org/I48379061"],"apc_list":null,"apc_paid":null,"fwci":0.363,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.56646896,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"40","issue":"7","first_page":null,"last_page":null},"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/T12661","display_name":"Iterative Methods for Nonlinear Equations","score":0.9817000031471252,"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/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.977400004863739,"subfield":{"id":"https://openalex.org/subfields/1804","display_name":"Statistics, Probability and Uncertainty"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7792842984199524},{"id":"https://openalex.org/keywords/fredholm-integral-equation","display_name":"Fredholm integral equation","score":0.7317699193954468},{"id":"https://openalex.org/keywords/volterra-integral-equation","display_name":"Volterra integral equation","score":0.6648538112640381},{"id":"https://openalex.org/keywords/kernel","display_name":"Kernel (algebra)","score":0.6143293976783752},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.6024017333984375},{"id":"https://openalex.org/keywords/integral-equation","display_name":"Integral equation","score":0.6016029119491577},{"id":"https://openalex.org/keywords/legendre-polynomials","display_name":"Legendre polynomials","score":0.597506046295166},{"id":"https://openalex.org/keywords/least-squares-function-approximation","display_name":"Least-squares function approximation","score":0.5585461854934692},{"id":"https://openalex.org/keywords/least-squares-support-vector-machine","display_name":"Least squares support vector machine","score":0.5065571069717407},{"id":"https://openalex.org/keywords/residual","display_name":"Residual","score":0.4795477092266083},{"id":"https://openalex.org/keywords/support-vector-machine","display_name":"Support vector machine","score":0.45747920870780945},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.4405099153518677},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.4259151220321655},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.41941526532173157},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3248441815376282},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.1987133026123047},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.1923159956932068},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.07346636056900024}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7792842984199524},{"id":"https://openalex.org/C89285879","wikidata":"https://www.wikidata.org/wiki/Q2991898","display_name":"Fredholm integral equation","level":3,"score":0.7317699193954468},{"id":"https://openalex.org/C21965488","wikidata":"https://www.wikidata.org/wiki/Q2632613","display_name":"Volterra integral equation","level":3,"score":0.6648538112640381},{"id":"https://openalex.org/C74193536","wikidata":"https://www.wikidata.org/wiki/Q574844","display_name":"Kernel (algebra)","level":2,"score":0.6143293976783752},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.6024017333984375},{"id":"https://openalex.org/C27016315","wikidata":"https://www.wikidata.org/wiki/Q580101","display_name":"Integral equation","level":2,"score":0.6016029119491577},{"id":"https://openalex.org/C111458787","wikidata":"https://www.wikidata.org/wiki/Q215405","display_name":"Legendre polynomials","level":2,"score":0.597506046295166},{"id":"https://openalex.org/C9936470","wikidata":"https://www.wikidata.org/wiki/Q6510405","display_name":"Least-squares function approximation","level":3,"score":0.5585461854934692},{"id":"https://openalex.org/C145828037","wikidata":"https://www.wikidata.org/wiki/Q17086219","display_name":"Least squares support vector machine","level":3,"score":0.5065571069717407},{"id":"https://openalex.org/C155512373","wikidata":"https://www.wikidata.org/wiki/Q287450","display_name":"Residual","level":2,"score":0.4795477092266083},{"id":"https://openalex.org/C12267149","wikidata":"https://www.wikidata.org/wiki/Q282453","display_name":"Support vector machine","level":2,"score":0.45747920870780945},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.4405099153518677},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.4259151220321655},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.41941526532173157},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3248441815376282},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.1987133026123047},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1923159956932068},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.07346636056900024},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","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/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s40314-021-01471-0","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s40314-021-01471-0","pdf_url":null,"source":{"id":"https://openalex.org/S4210195884","display_name":"Computational and Applied Mathematics","issn_l":"1807-0302","issn":["1807-0302","2238-3603"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computational and Applied Mathematics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G7923896936","display_name":null,"funder_award_id":"96011359","funder_id":"https://openalex.org/F4320322243","funder_display_name":"Iran National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320322243","display_name":"Iran National Science Foundation","ror":"https://ror.org/03sr1ma14"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":55,"referenced_works":["https://openalex.org/W640428934","https://openalex.org/W1496317909","https://openalex.org/W1596717185","https://openalex.org/W1663973292","https://openalex.org/W1901616594","https://openalex.org/W1970346034","https://openalex.org/W1994582952","https://openalex.org/W1995864261","https://openalex.org/W2000625825","https://openalex.org/W2002689747","https://openalex.org/W2005195748","https://openalex.org/W2016900451","https://openalex.org/W2017125096","https://openalex.org/W2017368465","https://openalex.org/W2018893257","https://openalex.org/W2020087720","https://openalex.org/W2026656818","https://openalex.org/W2029153938","https://openalex.org/W2029302017","https://openalex.org/W2031628517","https://openalex.org/W2032928866","https://openalex.org/W2037495825","https://openalex.org/W2042176466","https://openalex.org/W2048838035","https://openalex.org/W2051536688","https://openalex.org/W2052501514","https://openalex.org/W2061722333","https://openalex.org/W2061871845","https://openalex.org/W2071849871","https://openalex.org/W2076449788","https://openalex.org/W2077379345","https://openalex.org/W2093643421","https://openalex.org/W2146789435","https://openalex.org/W2219030831","https://openalex.org/W2260482700","https://openalex.org/W2332252290","https://openalex.org/W2405571875","https://openalex.org/W2476507202","https://openalex.org/W2585724693","https://openalex.org/W2606003931","https://openalex.org/W2607439077","https://openalex.org/W2749028154","https://openalex.org/W2767402708","https://openalex.org/W2780231556","https://openalex.org/W2803629276","https://openalex.org/W2804840443","https://openalex.org/W2892419861","https://openalex.org/W2901409391","https://openalex.org/W2966582106","https://openalex.org/W2998806258","https://openalex.org/W3003260192","https://openalex.org/W3041481472","https://openalex.org/W4212863985","https://openalex.org/W4246120546","https://openalex.org/W4253937035"],"related_works":["https://openalex.org/W4328008874","https://openalex.org/W39027593","https://openalex.org/W2401195586","https://openalex.org/W2184420462","https://openalex.org/W4293546845","https://openalex.org/W2157039219","https://openalex.org/W2003647985","https://openalex.org/W2015431139","https://openalex.org/W1963674083","https://openalex.org/W2140039100"],"abstract_inverted_index":null,"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}