{"id":"https://openalex.org/W3033336523","doi":"https://doi.org/10.1007/s40314-020-01198-4","title":"Using Bernstein multi-scaling polynomials to obtain numerical solution of Volterra integral equations system","display_name":"Using Bernstein multi-scaling polynomials to obtain numerical solution of Volterra integral equations system","publication_year":2020,"publication_date":"2020-06-06","ids":{"openalex":"https://openalex.org/W3033336523","doi":"https://doi.org/10.1007/s40314-020-01198-4","mag":"3033336523"},"language":"en","primary_location":{"id":"doi:10.1007/s40314-020-01198-4","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s40314-020-01198-4","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/A5032786276","display_name":"Alireza Yaghoobnia","orcid":"https://orcid.org/0000-0002-6372-1556"},"institutions":[{"id":"https://openalex.org/I204588832","display_name":"Islamic Azad University, Karaj","ror":"https://ror.org/01y4xm534","country_code":"IR","type":"education","lineage":["https://openalex.org/I110525433","https://openalex.org/I204588832"]}],"countries":["IR"],"is_corresponding":true,"raw_author_name":"A. R. Yaghoobnia","raw_affiliation_strings":["Department of Mathematics, Karaj Branch, Islamic Azad University, Karaj, Iran"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Karaj Branch, Islamic Azad University, Karaj, Iran","institution_ids":["https://openalex.org/I204588832"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5063871868","display_name":"R. Ezzati","orcid":"https://orcid.org/0000-0002-3162-6212"},"institutions":[{"id":"https://openalex.org/I204588832","display_name":"Islamic Azad University, Karaj","ror":"https://ror.org/01y4xm534","country_code":"IR","type":"education","lineage":["https://openalex.org/I110525433","https://openalex.org/I204588832"]}],"countries":["IR"],"is_corresponding":false,"raw_author_name":"R. Ezzati","raw_affiliation_strings":["Department of Mathematics, Karaj Branch, Islamic Azad University, Karaj, Iran"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Karaj Branch, Islamic Azad University, Karaj, Iran","institution_ids":["https://openalex.org/I204588832"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5032786276"],"corresponding_institution_ids":["https://openalex.org/I204588832"],"apc_list":null,"apc_paid":null,"fwci":0.1051,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.49341592,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"39","issue":"3","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":0.9973000288009644,"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/T11191","display_name":"Mathematical functions and polynomials","score":0.9890000224113464,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.729042112827301},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.7007018327713013},{"id":"https://openalex.org/keywords/bernstein-polynomial","display_name":"Bernstein polynomial","score":0.6746935844421387},{"id":"https://openalex.org/keywords/integral-equation","display_name":"Integral equation","score":0.597147524356842},{"id":"https://openalex.org/keywords/scaling","display_name":"Scaling","score":0.5913882255554199},{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.5676323771476746},{"id":"https://openalex.org/keywords/volterra-integral-equation","display_name":"Volterra integral equation","score":0.5540909171104431},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.49658042192459106},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.48034512996673584},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.08797633647918701},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.061957746744155884}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.729042112827301},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.7007018327713013},{"id":"https://openalex.org/C34179328","wikidata":"https://www.wikidata.org/wiki/Q826841","display_name":"Bernstein polynomial","level":2,"score":0.6746935844421387},{"id":"https://openalex.org/C27016315","wikidata":"https://www.wikidata.org/wiki/Q580101","display_name":"Integral equation","level":2,"score":0.597147524356842},{"id":"https://openalex.org/C99844830","wikidata":"https://www.wikidata.org/wiki/Q102441924","display_name":"Scaling","level":2,"score":0.5913882255554199},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.5676323771476746},{"id":"https://openalex.org/C21965488","wikidata":"https://www.wikidata.org/wiki/Q2632613","display_name":"Volterra integral equation","level":3,"score":0.5540909171104431},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.49658042192459106},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.48034512996673584},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.08797633647918701},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.061957746744155884},{"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:10.1007/s40314-020-01198-4","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s40314-020-01198-4","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":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":31,"referenced_works":["https://openalex.org/W628450978","https://openalex.org/W652921267","https://openalex.org/W1586051660","https://openalex.org/W1963636474","https://openalex.org/W1963906656","https://openalex.org/W1972165863","https://openalex.org/W1980564965","https://openalex.org/W1986135243","https://openalex.org/W2006660701","https://openalex.org/W2024882988","https://openalex.org/W2045663325","https://openalex.org/W2055102513","https://openalex.org/W2056624816","https://openalex.org/W2064241112","https://openalex.org/W2065170087","https://openalex.org/W2065451462","https://openalex.org/W2088862817","https://openalex.org/W2089271664","https://openalex.org/W2094253393","https://openalex.org/W2107221565","https://openalex.org/W2125982213","https://openalex.org/W2130978824","https://openalex.org/W2164619276","https://openalex.org/W2313644647","https://openalex.org/W2531136704","https://openalex.org/W2553506003","https://openalex.org/W2556641667","https://openalex.org/W2560846774","https://openalex.org/W2783829946","https://openalex.org/W4230278521","https://openalex.org/W4230445183"],"related_works":["https://openalex.org/W2517687681","https://openalex.org/W2118560105","https://openalex.org/W2358959122","https://openalex.org/W4225984655","https://openalex.org/W2031624200","https://openalex.org/W1539637428","https://openalex.org/W2754932876","https://openalex.org/W1541040149","https://openalex.org/W1826865795","https://openalex.org/W325682659"],"abstract_inverted_index":null,"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2020,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
