{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,1]],"date-time":"2026-06-01T18:18:56Z","timestamp":1780337936223,"version":"3.54.1"},"reference-count":34,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2024,7,26]],"date-time":"2024-07-26T00:00:00Z","timestamp":1721952000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>This study aims to find the numerical solution of the Rosenau\u2013Hyman and Fornberg\u2013Whitham equations via the quintic B-spline collocation method. Quintic B-spline, along with finite difference and theta-weighted schemes, is used for the discretization and approximation purposes. The effectiveness and robustness of the procedure is assessed by comparing the computed results with the exact and available results in the literature using absolute and relative error norms. The stability of the proposed scheme is studied using von Neumann stability analysis. Graphical representations are drawn to analyze the behavior of the solution.<\/jats:p>","DOI":"10.3390\/axioms13080501","type":"journal-article","created":{"date-parts":[[2024,7,26]],"date-time":"2024-07-26T13:04:59Z","timestamp":1721999099000},"page":"501","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Numerical Solution of Third-Order Rosenau\u2013Hyman and Fornberg\u2013Whitham Equations via B-Spline Interpolation Approach"],"prefix":"10.3390","volume":"13","author":[{"given":"Tanveer","family":"Akbar","sequence":"first","affiliation":[{"name":"Faculty of Engineering Sciences, GIK Institute, Topi 23640, Pakistan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Sirajul","family":"Haq","sequence":"additional","affiliation":[{"name":"Faculty of Engineering Sciences, GIK Institute, Topi 23640, Pakistan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9222-7610","authenticated-orcid":false,"given":"Shams Ul","family":"Arifeen","sequence":"additional","affiliation":[{"name":"Department of Sciences and Humanities, National University of Computer and Emerging Sciences, Peshawar 25000, Pakistan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5103-6092","authenticated-orcid":false,"given":"Azhar","family":"Iqbal","sequence":"additional","affiliation":[{"name":"Mathematics and Natural Sciences, Prince Mohammad Bin Fahd University, Al Khobar 31952, Saudi Arabia"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2024,7,26]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"691","DOI":"10.3934\/nhm.2012.7.691","article-title":"PDE problems arising in mathematical biology","volume":"7","author":"Friedman","year":"2012","journal-title":"Netw. 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