{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T01:18:17Z","timestamp":1760059097602,"version":"build-2065373602"},"reference-count":32,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2025,5,22]],"date-time":"2025-05-22T00:00:00Z","timestamp":1747872000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"the Talent Program of Chengdu Technological University","award":["2024RC021","25CAFUC03055"],"award-info":[{"award-number":["2024RC021","25CAFUC03055"]}]},{"name":"the Fundamental Research Funds for the Central Universities of Civil Aviation Flight University of China","award":["2024RC021","25CAFUC03055"],"award-info":[{"award-number":["2024RC021","25CAFUC03055"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>A novel two\u2013level linearized conservative finite difference method is proposed for solving the initial boundary value problem of the Rosenau\u2013RLW equation. To preserve the energy conservation property, the Crank\u2013Nicolson scheme is employed for temporal discretization, combined with an averaging treatment of the nonlinear term between the nth and (n+1)th time levels. For spatial discretization, a centered symmetric scheme is adopted. Meanwhile, the discrete conservation law is presented, and the existence and uniqueness of the numerical solutions are rigorously proved. Furthermore, the convergence and stability of the scheme are analyzed using the discrete energy method. Numerical experiments validate the theoretical results.<\/jats:p>","DOI":"10.3390\/axioms14060395","type":"journal-article","created":{"date-parts":[[2025,5,22]],"date-time":"2025-05-22T08:49:57Z","timestamp":1747903797000},"page":"395","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["A Linearized Conservative Finite Difference Scheme for the Rosenau\u2013RLW Equation"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0009-0007-7803-9887","authenticated-orcid":false,"given":"Yongzheng","family":"Li","sequence":"first","affiliation":[{"name":"Faculty of Science, Civil Aviation Flight University of China, Guanghan 618307, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0009-0005-1184-5839","authenticated-orcid":false,"given":"Longcheng","family":"Ren","sequence":"additional","affiliation":[{"name":"Faculty of Science, Civil Aviation Flight University of China, Guanghan 618307, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0009-0007-8106-9972","authenticated-orcid":false,"given":"Jinsong","family":"Hu","sequence":"additional","affiliation":[{"name":"College of Big Data and Artificial Intelligence, Chengdu Technological University, Chengdu 6111730, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9380-4558","authenticated-orcid":false,"given":"Kelong","family":"Zheng","sequence":"additional","affiliation":[{"name":"Faculty of Science, Civil Aviation Flight University of China, Guanghan 618307, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2025,5,22]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"321","DOI":"10.1017\/S0022112066001678","article-title":"Calculations of the development of an undular bore","volume":"25","author":"Peregrine","year":"1966","journal-title":"J. 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