{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,12]],"date-time":"2026-02-12T14:37:12Z","timestamp":1770907032137,"version":"3.50.1"},"reference-count":32,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2024,5,22]],"date-time":"2024-05-22T00:00:00Z","timestamp":1716336000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Natural Science Foundation of Shaanxi Province of China","award":["2024JC-YBMS-014"],"award-info":[{"award-number":["2024JC-YBMS-014"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>This paper presents a nonstandard numerical manifold method (NMM) for solving Burgers\u2019 equation. Employing the characteristic Galerkin method, we initially apply the Crank\u2013Nicolson method for temporal discretization along the characteristic. Subsequently, utilizing the Taylor expansion, we transform the semi-implicit formula into a fully explicit form. For spacial discretization, we construct the NMM dual-cover system tailored to Burgers\u2019 equation. We choose constant cover functions and first-order weight functions to enhance computational efficiency and exactly import boundary constraints. Finally, the integrated computing scheme is derived by using the standard Galerkin method, along with a Thomas algorithm-based solution procedure. The proposed method is verified through six benchmark numerical examples under various initial boundary conditions. Extensive comparisons with analytical solutions and results from alternative methods are conducted, demonstrating the accuracy and stability of our approach, particularly in solving Burgers\u2019 equation at high Reynolds numbers.<\/jats:p>","DOI":"10.3390\/axioms13060343","type":"journal-article","created":{"date-parts":[[2024,5,22]],"date-time":"2024-05-22T10:00:11Z","timestamp":1716372011000},"page":"343","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Explicit Numerical Manifold Characteristic Galerkin Method for Solving Burgers\u2019 Equation"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8829-8168","authenticated-orcid":false,"given":"Yue","family":"Sun","sequence":"first","affiliation":[{"name":"Institute of Computational Mathematics, Shaanxi University of Technology, Hanzhong 723001, China"},{"name":"School of Mathematics and Computer Science, Shaanxi University of Technology, Hanzhong 723001, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0009-0003-2414-6100","authenticated-orcid":false,"given":"Qian","family":"Chen","sequence":"additional","affiliation":[{"name":"Institute of Computational Mathematics, Shaanxi University of Technology, Hanzhong 723001, China"},{"name":"School of Mathematics and Computer Science, Shaanxi University of Technology, Hanzhong 723001, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Tao","family":"Chen","sequence":"additional","affiliation":[{"name":"School of Mathematics and Computer Science, Shaanxi University of Technology, Hanzhong 723001, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9679-1446","authenticated-orcid":false,"given":"Longquan","family":"Yong","sequence":"additional","affiliation":[{"name":"School of Mathematics and Computer Science, Shaanxi University of Technology, Hanzhong 723001, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2024,5,22]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"171","DOI":"10.1016\/S0065-2156(08)70100-5","article-title":"A mathematical model illustrating the theory of turbulence","volume":"1","author":"Burgers","year":"1948","journal-title":"Adv. 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