{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T01:17:32Z","timestamp":1760059052301,"version":"build-2065373602"},"reference-count":11,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2025,5,15]],"date-time":"2025-05-15T00:00:00Z","timestamp":1747267200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100012190","name":"Ministry of Science and Higher Education of the Russian Federation","doi-asserted-by":"publisher","award":["FZZS-2024-0003"],"award-info":[{"award-number":["FZZS-2024-0003"]}],"id":[{"id":"10.13039\/501100012190","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Computation"],"abstract":"<jats:p>Loaded Volterra integral equations represent a novel class of integral equations that have attracted considerable attention in recent years due to their numerous applications in various fields of science and engineering. This class of Volterra integral equations is characterized by the presence of a loading function, which complicates their theoretical and numerical analysis. In this paper, we study Volterra equations with locally loaded integral operators. The existence and uniqueness of their solutions are examined. A collocation-type method for the approximate solution of such equations is proposed, based on piecewise linear approximation of the exact solution. To confirm the convergence of the method, several numerical results for solving model problems are provided.<\/jats:p>","DOI":"10.3390\/computation13050121","type":"journal-article","created":{"date-parts":[[2025,5,15]],"date-time":"2025-05-15T07:46:49Z","timestamp":1747295209000},"page":"121","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Numerical Solution of Locally Loaded Volterra Integral Equations"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0009-0007-0488-2724","authenticated-orcid":false,"given":"Vladislav","family":"Byankin","sequence":"first","affiliation":[{"name":"Melentiev Energy Systems Institute of Siberian Branch of the Russian Academy of Sciences, Irkutsk 664033, Russia"},{"name":"Industrial Mathematics Lab, Baikal School of BRICS, Irkutsk National Research Technical University, Irkutsk 664074, Russia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6023-9847","authenticated-orcid":false,"given":"Aleksandr","family":"Tynda","sequence":"additional","affiliation":[{"name":"Higher and Applied Mathematics Department, Penza State University, Penza 440026, Russia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3131-1325","authenticated-orcid":false,"given":"Denis","family":"Sidorov","sequence":"additional","affiliation":[{"name":"Melentiev Energy Systems Institute of Siberian Branch of the Russian Academy of Sciences, Irkutsk 664033, Russia"},{"name":"Industrial Mathematics Lab, Baikal School of BRICS, Irkutsk National Research Technical University, Irkutsk 664074, Russia"},{"name":"School of Electrical Engineering and Automation, Harbin Institute of Technology, Harbin 150001, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5032-0665","authenticated-orcid":false,"given":"Aliona","family":"Dreglea","sequence":"additional","affiliation":[{"name":"Industrial Mathematics Lab, Baikal School of BRICS, Irkutsk National Research Technical University, Irkutsk 664074, Russia"},{"name":"School of Electrical Engineering and Automation, Harbin Institute of Technology, Harbin 150001, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2025,5,15]]},"reference":[{"key":"ref_1","unstructured":"Nakhushev, A.M. 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Math."}],"container-title":["Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2079-3197\/13\/5\/121\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,9]],"date-time":"2025-10-09T17:33:15Z","timestamp":1760031195000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2079-3197\/13\/5\/121"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,5,15]]},"references-count":11,"journal-issue":{"issue":"5","published-online":{"date-parts":[[2025,5]]}},"alternative-id":["computation13050121"],"URL":"https:\/\/doi.org\/10.3390\/computation13050121","relation":{},"ISSN":["2079-3197"],"issn-type":[{"type":"electronic","value":"2079-3197"}],"subject":[],"published":{"date-parts":[[2025,5,15]]}}}