{"id":"https://openalex.org/W4410405253","doi":"https://doi.org/10.3390/computation13050121","title":"Numerical Solution of Locally Loaded Volterra Integral Equations","display_name":"Numerical Solution of Locally Loaded Volterra Integral Equations","publication_year":2025,"publication_date":"2025-05-15","ids":{"openalex":"https://openalex.org/W4410405253","doi":"https://doi.org/10.3390/computation13050121"},"language":"en","primary_location":{"id":"doi:10.3390/computation13050121","is_oa":true,"landing_page_url":"https://doi.org/10.3390/computation13050121","pdf_url":"https://www.mdpi.com/2079-3197/13/5/121/pdf?version=1747308165","source":{"id":"https://openalex.org/S2738402919","display_name":"Computation","issn_l":"2079-3197","issn":["2079-3197"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computation","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2079-3197/13/5/121/pdf?version=1747308165","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5093532919","display_name":"Vladislav Byankin","orcid":"https://orcid.org/0009-0007-0488-2724"},"institutions":[{"id":"https://openalex.org/I4210114158","display_name":"Melentiev Energy Systems Institute","ror":"https://ror.org/02726j593","country_code":"RU","type":"facility","lineage":["https://openalex.org/I1313323035","https://openalex.org/I4210114158","https://openalex.org/I4210164537"]},{"id":"https://openalex.org/I4210122217","display_name":"Irkutsk National Research Technical University","ror":"https://ror.org/01zzkcm34","country_code":"RU","type":"education","lineage":["https://openalex.org/I4210122217"]}],"countries":["RU"],"is_corresponding":false,"raw_author_name":"Vladislav Byankin","raw_affiliation_strings":["Industrial Mathematics Lab, Baikal School of BRICS, Irkutsk National Research Technical University, Irkutsk 664074, Russia","Melentiev Energy Systems Institute of Siberian Branch of the Russian Academy of Sciences, Irkutsk 664033, Russia"],"raw_orcid":"https://orcid.org/0009-0007-0488-2724","affiliations":[{"raw_affiliation_string":"Industrial Mathematics Lab, Baikal School of BRICS, Irkutsk National Research Technical University, Irkutsk 664074, Russia","institution_ids":["https://openalex.org/I4210122217"]},{"raw_affiliation_string":"Melentiev Energy Systems Institute of Siberian Branch of the Russian Academy of Sciences, Irkutsk 664033, Russia","institution_ids":["https://openalex.org/I4210114158"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5030518548","display_name":"Aleksandr Tynda","orcid":"https://orcid.org/0000-0001-6023-9847"},"institutions":[{"id":"https://openalex.org/I114616248","display_name":"Penza State University","ror":"https://ror.org/056r5vk88","country_code":"RU","type":"education","lineage":["https://openalex.org/I114616248"]}],"countries":["RU"],"is_corresponding":false,"raw_author_name":"Aleksandr Tynda","raw_affiliation_strings":["Higher and Applied Mathematics Department, Penza State University, Penza 440026, Russia"],"raw_orcid":"https://orcid.org/0000-0001-6023-9847","affiliations":[{"raw_affiliation_string":"Higher and Applied Mathematics Department, Penza State University, Penza 440026, Russia","institution_ids":["https://openalex.org/I114616248"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5084429273","display_name":"Denis Sidorov","orcid":"https://orcid.org/0000-0002-3131-1325"},"institutions":[{"id":"https://openalex.org/I204983213","display_name":"Harbin Institute of Technology","ror":"https://ror.org/01yqg2h08","country_code":"CN","type":"education","lineage":["https://openalex.org/I204983213"]},{"id":"https://openalex.org/I4210114158","display_name":"Melentiev Energy Systems Institute","ror":"https://ror.org/02726j593","country_code":"RU","type":"facility","lineage":["https://openalex.org/I1313323035","https://openalex.org/I4210114158","https://openalex.org/I4210164537"]},{"id":"https://openalex.org/I4210122217","display_name":"Irkutsk National Research Technical University","ror":"https://ror.org/01zzkcm34","country_code":"RU","type":"education","lineage":["https://openalex.org/I4210122217"]}],"countries":["CN","RU"],"is_corresponding":true,"raw_author_name":"Denis Sidorov","raw_affiliation_strings":["Industrial Mathematics Lab, Baikal School of BRICS, Irkutsk National Research Technical University, Irkutsk 664074, Russia","Melentiev Energy Systems Institute of Siberian Branch of the Russian Academy of Sciences, Irkutsk 664033, Russia","School of Electrical Engineering and Automation, Harbin Institute of Technology, Harbin 150001, China"],"raw_orcid":"https://orcid.org/0000-0002-3131-1325","affiliations":[{"raw_affiliation_string":"Industrial Mathematics Lab, Baikal School of BRICS, Irkutsk National Research Technical University, Irkutsk 664074, Russia","institution_ids":["https://openalex.org/I4210122217"]},{"raw_affiliation_string":"Melentiev Energy Systems Institute of Siberian Branch of the Russian Academy of Sciences, Irkutsk 664033, Russia","institution_ids":["https://openalex.org/I4210114158"]},{"raw_affiliation_string":"School of Electrical Engineering and Automation, Harbin Institute of Technology, Harbin 150001, China","institution_ids":["https://openalex.org/I204983213"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5059347972","display_name":"Aliona Dreglea","orcid":"https://orcid.org/0000-0002-5032-0665"},"institutions":[{"id":"https://openalex.org/I204983213","display_name":"Harbin Institute of Technology","ror":"https://ror.org/01yqg2h08","country_code":"CN","type":"education","lineage":["https://openalex.org/I204983213"]},{"id":"https://openalex.org/I4210122217","display_name":"Irkutsk National Research Technical University","ror":"https://ror.org/01zzkcm34","country_code":"RU","type":"education","lineage":["https://openalex.org/I4210122217"]}],"countries":["CN","RU"],"is_corresponding":false,"raw_author_name":"Aliona Dreglea","raw_affiliation_strings":["Industrial Mathematics Lab, Baikal School of BRICS, Irkutsk National Research Technical University, Irkutsk 664074, Russia","School of Electrical Engineering and Automation, Harbin Institute of Technology, Harbin 150001, China"],"raw_orcid":"https://orcid.org/0000-0002-5032-0665","affiliations":[{"raw_affiliation_string":"Industrial Mathematics Lab, Baikal School of BRICS, Irkutsk National Research Technical University, Irkutsk 664074, Russia","institution_ids":["https://openalex.org/I4210122217"]},{"raw_affiliation_string":"School of Electrical Engineering and Automation, Harbin Institute of Technology, Harbin 150001, China","institution_ids":["https://openalex.org/I204983213"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5084429273"],"corresponding_institution_ids":["https://openalex.org/I204983213","https://openalex.org/I4210114158","https://openalex.org/I4210122217"],"apc_list":{"value":1400,"currency":"CHF","value_usd":1515},"apc_paid":{"value":1400,"currency":"CHF","value_usd":1515},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.14976217,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"13","issue":"5","first_page":"121","last_page":"121"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11205","display_name":"Numerical methods in inverse problems","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/T11205","display_name":"Numerical methods in inverse problems","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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":0.9991999864578247,"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"}},{"id":"https://openalex.org/T12727","display_name":"Differential Equations and Numerical Methods","score":0.9991000294685364,"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/volterra-integral-equation","display_name":"Volterra integral equation","score":0.8662898540496826},{"id":"https://openalex.org/keywords/integral-equation","display_name":"Integral equation","score":0.7438364028930664},{"id":"https://openalex.org/keywords/volterra-equations","display_name":"Volterra equations","score":0.5845785140991211},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.523494303226471},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4348657727241516},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3926331400871277},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.2042718231678009},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.17510607838630676}],"concepts":[{"id":"https://openalex.org/C21965488","wikidata":"https://www.wikidata.org/wiki/Q2632613","display_name":"Volterra integral equation","level":3,"score":0.8662898540496826},{"id":"https://openalex.org/C27016315","wikidata":"https://www.wikidata.org/wiki/Q580101","display_name":"Integral equation","level":2,"score":0.7438364028930664},{"id":"https://openalex.org/C2983756050","wikidata":"https://www.wikidata.org/wiki/Q150052","display_name":"Volterra equations","level":3,"score":0.5845785140991211},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.523494303226471},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4348657727241516},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3926331400871277},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.2042718231678009},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.17510607838630676},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.3390/computation13050121","is_oa":true,"landing_page_url":"https://doi.org/10.3390/computation13050121","pdf_url":"https://www.mdpi.com/2079-3197/13/5/121/pdf?version=1747308165","source":{"id":"https://openalex.org/S2738402919","display_name":"Computation","issn_l":"2079-3197","issn":["2079-3197"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computation","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:06c944a0f29843ddbfe0935302ca252c","is_oa":true,"landing_page_url":"https://doaj.org/article/06c944a0f29843ddbfe0935302ca252c","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Computation, Vol 13, Iss 5, p 121 (2025)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/computation13050121","is_oa":true,"landing_page_url":"https://doi.org/10.3390/computation13050121","pdf_url":"https://www.mdpi.com/2079-3197/13/5/121/pdf?version=1747308165","source":{"id":"https://openalex.org/S2738402919","display_name":"Computation","issn_l":"2079-3197","issn":["2079-3197"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computation","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G6806780606","display_name":null,"funder_award_id":"FZZS-2024-0003","funder_id":"https://openalex.org/F4320327494","funder_display_name":"Ministry of Science and Higher Education of the Russian Federation"}],"funders":[{"id":"https://openalex.org/F4320327494","display_name":"Ministry of Science and Higher Education of the Russian Federation","ror":null}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4410405253.pdf","grobid_xml":"https://content.openalex.org/works/W4410405253.grobid-xml"},"referenced_works_count":6,"referenced_works":["https://openalex.org/W1979318803","https://openalex.org/W4221130126","https://openalex.org/W4327648066","https://openalex.org/W4391068806","https://openalex.org/W6850391619","https://openalex.org/W6860918965"],"related_works":["https://openalex.org/W2082102072","https://openalex.org/W2517687681","https://openalex.org/W2118560105","https://openalex.org/W2358959122","https://openalex.org/W4401089097","https://openalex.org/W4249149186","https://openalex.org/W4225984655","https://openalex.org/W2031624200","https://openalex.org/W1541040149","https://openalex.org/W1539637428"],"abstract_inverted_index":{"Loaded":[0],"Volterra":[1,34,58],"integral":[2,9,35,63],"equations":[3,10,36,59,83],"represent":[4],"a":[5,43],"novel":[6],"class":[7,32],"of":[8,27,33,42,69,81,91,99],"that":[11],"have":[12],"attracted":[13],"considerable":[14],"attention":[15],"in":[16,24],"recent":[17],"years":[18],"due":[19],"to":[20],"their":[21,48,70],"numerous":[22],"applications":[23],"various":[25],"fields":[26],"science":[28],"and":[29,50,67],"engineering.":[30],"This":[31],"is":[37,84],"characterized":[38],"by":[39],"the":[40,78,92,97,100],"presence":[41],"loading":[44],"function,":[45],"which":[46],"complicates":[47],"theoretical":[49],"numerical":[51,103],"analysis.":[52],"In":[53],"this":[54],"paper,":[55],"we":[56],"study":[57],"with":[60],"locally":[61],"loaded":[62],"operators.":[64],"The":[65],"existence":[66],"uniqueness":[68],"solutions":[71],"are":[72,109],"examined.":[73],"A":[74],"collocation-type":[75],"method":[76],"for":[77,105],"approximate":[79],"solution":[80],"such":[82],"proposed,":[85],"based":[86],"on":[87],"piecewise":[88],"linear":[89],"approximation":[90],"exact":[93],"solution.":[94],"To":[95],"confirm":[96],"convergence":[98],"method,":[101],"several":[102],"results":[104],"solving":[106],"model":[107],"problems":[108],"provided.":[110]},"counts_by_year":[],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}