{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,3]],"date-time":"2026-02-03T17:24:24Z","timestamp":1770139464983,"version":"3.49.0"},"reference-count":50,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2023,5,8]],"date-time":"2023-05-08T00:00:00Z","timestamp":1683504000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"C\u00e1tedra Primafrio-UPCT"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>The motive of this work is to provide the numerical performances of the reactive transport model that carries trucks with goods on roads by exploiting the stochastic procedures based on the Meyer wavelet (MW) neural network. An objective function is constructed by using the differential model and its boundary conditions. The optimization of the objective function is performed through the hybridization of the global and local search procedures, i.e., swarming and interior point algorithms. Three different cases of the model have been obtained, and the exactness of the stochastic procedure is observed by using the comparison of the obtained and Adams solutions. The negligible absolute error enhances the exactness of the proposed MW neural networks along with the hybridization of the global and local search schemes. Moreover, statistical interpretations based on different operators, histograms, and boxplots are provided to validate the constancy of the designed stochastic structure.<\/jats:p>","DOI":"10.3390\/axioms12050456","type":"journal-article","created":{"date-parts":[[2023,5,9]],"date-time":"2023-05-09T01:34:26Z","timestamp":1683596066000},"page":"456","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":12,"title":["A Swarming Meyer Wavelet Computing Approach to Solve the Transport System of Goods"],"prefix":"10.3390","volume":"12","author":[{"given":"Zulqurnain","family":"Sabir","sequence":"first","affiliation":[{"name":"Department of Mathematics and Statistics, Hazara University, Mansehra 21120, Pakistan"},{"name":"Department of Computer Science and Mathematics, Lebanese American University, Beirut 11022801, Lebanon"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0170-5286","authenticated-orcid":false,"given":"Tareq","family":"Saeed","sequence":"additional","affiliation":[{"name":"Financial Mathematics and Actuarial Science (FMAS)-Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2788-809X","authenticated-orcid":false,"given":"Juan L. G.","family":"Guirao","sequence":"additional","affiliation":[{"name":"Department of Applied Mathematics and Statistics, Technical University of Cartagena, Hospital de Marina, 30203 Cartagena, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Juan M.","family":"S\u00e1nchez","sequence":"additional","affiliation":[{"name":"Department of Applied Mathematics and Statistics, Technical University of Cartagena, Hospital de Marina, 30203 Cartagena, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Adri\u00e1n","family":"Valverde","sequence":"additional","affiliation":[{"name":"Department of Applied Mathematics and Statistics, Technical University of Cartagena, Hospital de Marina, 30203 Cartagena, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,5,8]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"637","DOI":"10.1016\/j.asej.2014.01.001","article-title":"On the multiplicity of solutions of the nonlinear reactive transport model","volume":"5","author":"Shivanian","year":"2014","journal-title":"Ain Shams Eng. 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