{"id":"https://openalex.org/W4412565054","doi":"https://doi.org/10.1016/j.matcom.2025.07.030","title":"A high accurate numerical framework for the solution of the vanishing-delay Volterra integro-differential equations via Legendre pseudo-spectral element approach","display_name":"A high accurate numerical framework for the solution of the vanishing-delay Volterra integro-differential equations via Legendre pseudo-spectral element approach","publication_year":2025,"publication_date":"2025-07-22","ids":{"openalex":"https://openalex.org/W4412565054","doi":"https://doi.org/10.1016/j.matcom.2025.07.030"},"language":"en","primary_location":{"id":"doi:10.1016/j.matcom.2025.07.030","is_oa":false,"landing_page_url":"https://doi.org/10.1016/j.matcom.2025.07.030","pdf_url":null,"source":{"id":"https://openalex.org/S32114090","display_name":"Mathematics and Computers in Simulation","issn_l":"0378-4754","issn":["0378-4754","1872-7166"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics and Computers in Simulation","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/A5024865406","display_name":"Yin Yang","orcid":"https://orcid.org/0000-0002-7435-152X"},"institutions":[{"id":"https://openalex.org/I4610292","display_name":"Xiangtan University","ror":"https://ror.org/00xsfaz62","country_code":"CN","type":"education","lineage":["https://openalex.org/I4610292"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yin Yang","raw_affiliation_strings":["School of Mathematics and Computational Science, Xiangtan University, National Center for Applied Mathematics in Hunan, Xiangtan 411105, Hunan, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Computational Science, Xiangtan University, National Center for Applied Mathematics in Hunan, Xiangtan 411105, Hunan, China","institution_ids":["https://openalex.org/I4610292"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Pai Yao","orcid":null},"institutions":[{"id":"https://openalex.org/I4610292","display_name":"Xiangtan University","ror":"https://ror.org/00xsfaz62","country_code":"CN","type":"education","lineage":["https://openalex.org/I4610292"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Pai Yao","raw_affiliation_strings":["School of Mathematics and Computational Science, Xiangtan University, Xiangtan 411105, Hunan, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Computational Science, Xiangtan University, Xiangtan 411105, Hunan, China","institution_ids":["https://openalex.org/I4610292"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5051458444","display_name":"Emran Tohidi","orcid":"https://orcid.org/0000-0001-7211-5307"},"institutions":[{"id":"https://openalex.org/I2800768525","display_name":"University of Bojnord","ror":"https://ror.org/05khxfe53","country_code":"IR","type":"education","lineage":["https://openalex.org/I2800768525"]},{"id":"https://openalex.org/I4210107575","display_name":"Kosar University of Bojnord","ror":"https://ror.org/01e7e7r31","country_code":"IR","type":"education","lineage":["https://openalex.org/I4210107575"]}],"countries":["IR"],"is_corresponding":true,"raw_author_name":"Emran Tohidi","raw_affiliation_strings":["Department of Mathematics, Kosar University of Bojnord, P.O. Box 94531-55168, Bojnord, Iran"],"raw_orcid":"https://orcid.org/0000-0001-7211-5307","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Kosar University of Bojnord, P.O. Box 94531-55168, Bojnord, Iran","institution_ids":["https://openalex.org/I4210107575","https://openalex.org/I2800768525"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5051458444"],"corresponding_institution_ids":["https://openalex.org/I2800768525","https://openalex.org/I4210107575"],"apc_list":{"value":1740,"currency":"USD","value_usd":1740},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.24298865,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"240","issue":null,"first_page":"403","last_page":"422"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12727","display_name":"Differential Equations and Numerical Methods","score":0.9998000264167786,"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":0.9998000264167786,"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":0.989799976348877,"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/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9796000123023987,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/legendre-polynomials","display_name":"Legendre polynomials","score":0.8930964469909668},{"id":"https://openalex.org/keywords/spectral-element-method","display_name":"Spectral element method","score":0.6294696927070618},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5853257179260254},{"id":"https://openalex.org/keywords/element","display_name":"Element (criminal law)","score":0.5663167238235474},{"id":"https://openalex.org/keywords/volterra-integral-equation","display_name":"Volterra integral equation","score":0.5414221286773682},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5291476845741272},{"id":"https://openalex.org/keywords/volterra-equations","display_name":"Volterra equations","score":0.476310133934021},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.470394492149353},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.46869635581970215},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.465128630399704},{"id":"https://openalex.org/keywords/differential","display_name":"Differential (mechanical device)","score":0.4223487377166748},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.26327797770500183},{"id":"https://openalex.org/keywords/integral-equation","display_name":"Integral equation","score":0.2388695776462555},{"id":"https://openalex.org/keywords/mixed-finite-element-method","display_name":"Mixed finite element method","score":0.21693286299705505},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.15343624353408813}],"concepts":[{"id":"https://openalex.org/C111458787","wikidata":"https://www.wikidata.org/wiki/Q215405","display_name":"Legendre polynomials","level":2,"score":0.8930964469909668},{"id":"https://openalex.org/C38961997","wikidata":"https://www.wikidata.org/wiki/Q7575186","display_name":"Spectral element method","level":4,"score":0.6294696927070618},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5853257179260254},{"id":"https://openalex.org/C200288055","wikidata":"https://www.wikidata.org/wiki/Q2621792","display_name":"Element (criminal law)","level":2,"score":0.5663167238235474},{"id":"https://openalex.org/C21965488","wikidata":"https://www.wikidata.org/wiki/Q2632613","display_name":"Volterra integral equation","level":3,"score":0.5414221286773682},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5291476845741272},{"id":"https://openalex.org/C2983756050","wikidata":"https://www.wikidata.org/wiki/Q150052","display_name":"Volterra equations","level":3,"score":0.476310133934021},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.470394492149353},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.46869635581970215},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.465128630399704},{"id":"https://openalex.org/C93226319","wikidata":"https://www.wikidata.org/wiki/Q193137","display_name":"Differential (mechanical device)","level":2,"score":0.4223487377166748},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.26327797770500183},{"id":"https://openalex.org/C27016315","wikidata":"https://www.wikidata.org/wiki/Q580101","display_name":"Integral equation","level":2,"score":0.2388695776462555},{"id":"https://openalex.org/C144468803","wikidata":"https://www.wikidata.org/wiki/Q16965966","display_name":"Mixed finite element method","level":3,"score":0.21693286299705505},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.15343624353408813},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1016/j.matcom.2025.07.030","is_oa":false,"landing_page_url":"https://doi.org/10.1016/j.matcom.2025.07.030","pdf_url":null,"source":{"id":"https://openalex.org/S32114090","display_name":"Mathematics and Computers in Simulation","issn_l":"0378-4754","issn":["0378-4754","1872-7166"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics and Computers in Simulation","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1832942644","display_name":null,"funder_award_id":"12261131501","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G627238494","display_name":null,"funder_award_id":"2024JJ1008","funder_id":"https://openalex.org/F4320321471","funder_display_name":"Hunan Provincial Science and Technology Department"},{"id":"https://openalex.org/G8418242333","display_name":null,"funder_award_id":"D23017","funder_id":"https://openalex.org/F4320327912","funder_display_name":"Higher Education Discipline Innovation Project"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320321471","display_name":"Hunan Provincial Science and Technology Department","ror":"https://ror.org/04qgr7x96"},{"id":"https://openalex.org/F4320327912","display_name":"Higher Education Discipline Innovation Project","ror":null},{"id":"https://openalex.org/F4320335801","display_name":"Science and Technology Innovative Research Team in Higher Educational Institutions of Hunan Province","ror":null}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":30,"referenced_works":["https://openalex.org/W640428934","https://openalex.org/W1035252786","https://openalex.org/W1550341792","https://openalex.org/W1567668233","https://openalex.org/W1977298783","https://openalex.org/W1979107452","https://openalex.org/W2024169233","https://openalex.org/W2057743217","https://openalex.org/W2070512346","https://openalex.org/W2083183137","https://openalex.org/W2145736329","https://openalex.org/W2187756587","https://openalex.org/W2244358154","https://openalex.org/W2258012589","https://openalex.org/W2318462232","https://openalex.org/W2588191062","https://openalex.org/W2947195175","https://openalex.org/W2965428548","https://openalex.org/W2970467412","https://openalex.org/W3208263433","https://openalex.org/W3216612220","https://openalex.org/W4247375400","https://openalex.org/W4394985164","https://openalex.org/W4399924231","https://openalex.org/W4406322727","https://openalex.org/W6627065209","https://openalex.org/W6686931628","https://openalex.org/W6766047460","https://openalex.org/W6804611180","https://openalex.org/W6876106983"],"related_works":["https://openalex.org/W2082102072","https://openalex.org/W3024058709","https://openalex.org/W4249149186","https://openalex.org/W1541040149","https://openalex.org/W128596308","https://openalex.org/W2038297679","https://openalex.org/W2184249577","https://openalex.org/W1539637428","https://openalex.org/W2600371480","https://openalex.org/W39027593"],"abstract_inverted_index":null,"counts_by_year":[],"updated_date":"2026-06-15T08:34:33.830935","created_date":"2025-10-10T00:00:00"}