{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,6]],"date-time":"2025-11-06T06:22:34Z","timestamp":1762410154055,"version":"build-2065373602"},"reference-count":52,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2023,3,8]],"date-time":"2023-03-08T00:00:00Z","timestamp":1678233600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Natural Science Foundation of China","award":["12171435"],"award-info":[{"award-number":["12171435"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>Second-order oscillatory problems have been found to be applicable in studying various phenomena in science and engineering; this is because these problems have the capabilities of replicating different aspects of the real world. In this research, a new hybrid method shall be formulated for the simulations of second-order oscillatory problems with applications to physical systems. The proposed method shall be formulated using the procedure of interpolation and collocation by adopting power series as basis function. In formulating the method, off-step points were introduced within the interval of integration in order to bypass the Dahlquist barrier, improve the accuracy of the method and also upgrade the order of consistence of the method. The paper further validated the some properties of the hybrid method derived and from the results obtained; the new method was found to be consistent, convergent and stable. The simulation results generated as a result of the application of the new method on some second-order oscillatory differential equations also showed that the new hybrid method is computationally reliable.<\/jats:p>","DOI":"10.3390\/axioms12030282","type":"journal-article","created":{"date-parts":[[2023,3,8]],"date-time":"2023-03-08T02:08:14Z","timestamp":1678241294000},"page":"282","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":12,"title":["On the Simulations of Second-Order Oscillatory Problems with Applications to Physical Systems"],"prefix":"10.3390","volume":"12","author":[{"given":"Lydia J.","family":"Kwari","sequence":"first","affiliation":[{"name":"Department of Mathematics, School of Sciences, Federal College of Education, Pankshin 933105, Nigeria"}],"role":[{"role":"author","vocab":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6304-4965","authenticated-orcid":false,"given":"Joshua","family":"Sunday","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Natural Sciences, University of Jos, Jos 930003, Nigeria"}],"role":[{"role":"author","vocab":"crossref"}]},{"given":"Joel N.","family":"Ndam","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Natural Sciences, University of Jos, Jos 930003, Nigeria"}],"role":[{"role":"author","vocab":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2699-1490","authenticated-orcid":false,"given":"Ali","family":"Shokri","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Sciences, University of Maragheh, Maragheh 83111-55181, Iran"}],"role":[{"role":"author","vocab":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4079-2850","authenticated-orcid":false,"given":"Yuanheng","family":"Wang","sequence":"additional","affiliation":[{"name":"College of Mathematics and Computer Science, Zhejiang Normal University, Jinhua 321004, China"}],"role":[{"role":"author","vocab":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,3,8]]},"reference":[{"key":"ref_1","first-page":"278","article-title":"The Cauchy problem for degenerate parabolic convolution equation","volume":"12","author":"Musaev","year":"2021","journal-title":"TWMS J. 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