{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,30]],"date-time":"2026-06-30T20:04:51Z","timestamp":1782849891345,"version":"3.54.5"},"reference-count":31,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2025,4,8]],"date-time":"2025-04-08T00:00:00Z","timestamp":1744070400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Talent Program of Chengdu Technological University","award":["2024RC021"],"award-info":[{"award-number":["2024RC021"]}]},{"name":"Talent Program of Chengdu Technological University","award":["PHD2023-047"],"award-info":[{"award-number":["PHD2023-047"]}]},{"name":"Talent Program of Chengdu Technological University","award":["gnzds201902"],"award-info":[{"award-number":["gnzds201902"]}]},{"name":"Fundamental Research Funds for the Central Universities of Civil Aviation Flight University of China","award":["2024RC021"],"award-info":[{"award-number":["2024RC021"]}]},{"name":"Fundamental Research Funds for the Central Universities of Civil Aviation Flight University of China","award":["PHD2023-047"],"award-info":[{"award-number":["PHD2023-047"]}]},{"name":"Fundamental Research Funds for the Central Universities of Civil Aviation Flight University of China","award":["gnzds201902"],"award-info":[{"award-number":["gnzds201902"]}]},{"name":"Opening Fund of Provincial Key Lab of Applied Nuclear Techniques in Geosciences","award":["2024RC021"],"award-info":[{"award-number":["2024RC021"]}]},{"name":"Opening Fund of Provincial Key Lab of Applied Nuclear Techniques in Geosciences","award":["PHD2023-047"],"award-info":[{"award-number":["PHD2023-047"]}]},{"name":"Opening Fund of Provincial Key Lab of Applied Nuclear Techniques in Geosciences","award":["gnzds201902"],"award-info":[{"award-number":["gnzds201902"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Two numerical methods are investigated for the initial\u2013boundary value problem of a nonlinear Rosenau\u2013KdV\u2013RLW equation with homogeneous boundary conditions. With the premise of achieving second-order theoretical accuracy in the temporal direction, two-level linearization discretization and three-level extrapolated linearization discretization are applied to nonlinear terms, respectively. To achieve a higher theoretical accuracy in the spatial direction, the Richardson extrapolation combination technique is employed; thereby, a two-level linearized difference scheme and a three-level linear difference scheme for the Rosenau\u2013KdV\u2013RLW equation are proposed, both with a theoretical accuracy of O(\u03c42+h4). The two-level difference scheme also reasonably simulates the conservation property of the problem. The convergence and stability of the two schemes are proven using mathematical induction and discrete functional analysis methods. The numerical results demonstrate the effectiveness of both schemes.<\/jats:p>","DOI":"10.3390\/sym17040566","type":"journal-article","created":{"date-parts":[[2025,4,10]],"date-time":"2025-04-10T05:28:07Z","timestamp":1744262887000},"page":"566","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Two High-Accuracy Linear Finite Difference Schemes for Rosenau\u2013KdV\u2013RLW Equation"],"prefix":"10.3390","volume":"17","author":[{"ORCID":"https:\/\/orcid.org\/0009-0007-8106-9972","authenticated-orcid":false,"given":"Jinsong","family":"Hu","sequence":"first","affiliation":[{"name":"College of Big Data and Artificial Intelligence, Chengdu Technological University, Chengdu 611730, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"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":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2027-0270","authenticated-orcid":false,"given":"Zhong","family":"Chen","sequence":"additional","affiliation":[{"name":"Key Laboratory of Nuclear Power Systems and Equipment, Shanghai Jiao Tong University, Shanghai 200030, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2025,4,8]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"422","DOI":"10.1080\/14786449508620739","article-title":"On the change of form of long waves advancing in a rectangular canal, and on a new type of long stationary waves","volume":"39","author":"Korteweg","year":"1895","journal-title":"Philos. 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