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The RBF contains three distinct layers as follows: the input layer including the elementary nodes; the second layer including the hidden layers via high dimensions; and the output layer for responding and activating the patterns of the input layer. The obtained results revealed that this method could solve and approximate such problems under acceptable confidence.<\/jats:p>","DOI":"10.1142\/s1793005726500444","type":"journal-article","created":{"date-parts":[[2025,1,10]],"date-time":"2025-01-10T10:08:31Z","timestamp":1736503711000},"page":"893-904","source":"Crossref","is-referenced-by-count":0,"title":["Solving Differential Equations with Z-Numbers Data by Gaussian Radial Basic Function"],"prefix":"10.1142","volume":"22","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7926-7477","authenticated-orcid":false,"given":"Leila","family":"Qalehe","sequence":"first","affiliation":[{"name":"Department of Applied Mathematics, North Tehran Branch, Islamic Azad University, Tehran, Iran"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5912-058X","authenticated-orcid":false,"given":"Mozhdeh Afshar","family":"Kermani","sequence":"additional","affiliation":[{"name":"Department of Applied Mathematics, North Tehran Branch, Islamic Azad University, Tehran, Iran"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3929-9762","authenticated-orcid":false,"given":"Tofigh","family":"Allahviranloo","sequence":"additional","affiliation":[{"name":"Department Faculty of Engineering and Natural Sciences, Istinye University, Istanbul, Turkey"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2025,2,26]]},"reference":[{"key":"S1793005726500444BIB001","doi-asserted-by":"publisher","DOI":"10.1016\/j.ins.2014.08.024"},{"key":"S1793005726500444BIB002","doi-asserted-by":"publisher","DOI":"10.1016\/S0096-3003(03)00160-7"},{"key":"S1793005726500444BIB003","doi-asserted-by":"publisher","DOI":"10.1109\/TSMC.1972.5408553"},{"key":"S1793005726500444BIB004","doi-asserted-by":"publisher","DOI":"10.1016\/S0165-0114(82)80001-8"},{"key":"S1793005726500444BIB005","doi-asserted-by":"publisher","DOI":"10.1016\/j.ins.2009.12.016"},{"key":"S1793005726500444BIB006","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-030-66501-2_72"},{"key":"S1793005726500444BIB007","first-page":"2807","volume":"7","author":"Kang B.","year":"2012","journal-title":"Journal of Computational Information Systems"},{"key":"S1793005726500444BIB008","doi-asserted-by":"publisher","DOI":"10.1016\/j.enganabound.2011.06.012"},{"key":"S1793005726500444BIB009","doi-asserted-by":"publisher","DOI":"10.1016\/0165-0114(87)90029-7"},{"key":"S1793005726500444BIB010","doi-asserted-by":"publisher","DOI":"10.1016\/S0898-1221(03)90151-9"},{"key":"S1793005726500444BIB011","doi-asserted-by":"publisher","DOI":"10.2528\/PIERB10062303"},{"key":"S1793005726500444BIB012","doi-asserted-by":"publisher","DOI":"10.1080\/00221689609498476"},{"key":"S1793005726500444BIB013","first-page":"86","volume":"6","author":"Esmaeilbeig M.","year":"2018","journal-title":"Computational Methods for Differential Equations"},{"key":"S1793005726500444BIB014","doi-asserted-by":"publisher","DOI":"10.1016\/j.enganabound.2012.12.002"},{"key":"S1793005726500444BIB015","doi-asserted-by":"publisher","DOI":"10.1016\/0165-0114(87)90030-3"},{"key":"S1793005726500444BIB016","first-page":"349","volume":"11","author":"Uddin M.","year":"2014","journal-title":"Walailak Journal of Science and Technology WJST"},{"key":"S1793005726500444BIB017","doi-asserted-by":"publisher","DOI":"10.1109\/72.701174"},{"key":"S1793005726500444BIB018","doi-asserted-by":"publisher","DOI":"10.1002\/int.21521"},{"key":"S1793005726500444BIB019","doi-asserted-by":"publisher","DOI":"10.1016\/j.ins.2011.02.022"},{"key":"S1793005726500444BIB020","doi-asserted-by":"publisher","DOI":"10.1016\/j.compstruc.2004.05.014"},{"key":"S1793005726500444BIB021","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-031-18347-8_3"},{"key":"S1793005726500444BIB022","doi-asserted-by":"publisher","DOI":"10.1016\/j.ins.2022.07.171"}],"container-title":["New Mathematics and Natural Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S1793005726500444","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,2,3]],"date-time":"2026-02-03T01:13:22Z","timestamp":1770081202000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/10.1142\/S1793005726500444"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,2,26]]},"references-count":22,"journal-issue":{"issue":"03","published-print":{"date-parts":[[2026,9]]}},"alternative-id":["10.1142\/S1793005726500444"],"URL":"https:\/\/doi.org\/10.1142\/s1793005726500444","relation":{},"ISSN":["1793-0057","1793-7027"],"issn-type":[{"value":"1793-0057","type":"print"},{"value":"1793-7027","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,2,26]]}}}