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R. China"}]},{"given":"Danxia","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Mathematics , 47846 Taiyuan University of Technology , Taiyuan , 030024, Shanxi , P. R. China"}]},{"given":"Hongen","family":"Jia","sequence":"additional","affiliation":[{"name":"School of Mathematics , 47846 Taiyuan University of Technology , Taiyuan , 030024, Shanxi , P. R. China"}]},{"given":"Chenhui","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Mathematics , 47846 Taiyuan University of Technology , Taiyuan , 030024, Shanxi , P. R. China"}]}],"member":"374","published-online":{"date-parts":[[2025,10,22]]},"reference":[{"doi-asserted-by":"crossref","unstructured":"R. An and C. Zhou,\nError analysis of a fractional-step method for magnetohydrodynamics equations,\nJ. Comput. Appl. Math. 313 (2017), 168\u2013184.","key":"2025123121114961163_j_cmam-2025-0046_ref_001","DOI":"10.1016\/j.cam.2016.09.005"},{"doi-asserted-by":"crossref","unstructured":"J. Becker,\nA second order backward difference method with variable steps for a parabolic problem,\nBIT 38 (1998), no. 4, 644\u2013662.","key":"2025123121114961163_j_cmam-2025-0046_ref_002","DOI":"10.1007\/BF02510406"},{"doi-asserted-by":"crossref","unstructured":"V. Bityurin, V. Zeigarnik and A. Kuranov,\nOn a perspective of mhd technology in aerospace applications,\n27th Plasma Dynamics and Lasers Conference,\nAAAI, New Orleans (1996), AAAI Paper 96-2355.","key":"2025123121114961163_j_cmam-2025-0046_ref_003","DOI":"10.2514\/6.1996-2355"},{"doi-asserted-by":"crossref","unstructured":"L. Bu, J. Wu, L. Mei and Y. Wang,\nSecond-order linear adaptive time-stepping schemes for the fractional Allen\u2013Cahn equation,\nComput. Math. Appl. 145 (2023), 260\u2013274.","key":"2025123121114961163_j_cmam-2025-0046_ref_004","DOI":"10.1016\/j.camwa.2023.06.027"},{"doi-asserted-by":"crossref","unstructured":"T. Chu, J. Wang, N. Wang and Z. Zhang,\nOptimal-order convergence of a two-step BDF method for the Navier\u2013Stokes equations with \n                  \n                     \n                        \n                           H\n                           1\n                        \n                     \n                     \n                     H^{1}\n                  \n                initial data,\nJ. Sci. Comput. 96 (2023), no. 2, Paper No. 62.","key":"2025123121114961163_j_cmam-2025-0046_ref_005","DOI":"10.1007\/s10915-023-02270-x"},{"doi-asserted-by":"crossref","unstructured":"D. Cordoba and C. Marliani,\nOn the behavior of hyperbolic netural points in two-dimensional ideal magnetohydrodynamics,\nProc. Natl. Acad. Sci. USA 96 (1999), no. 6, 2612\u20132614.","key":"2025123121114961163_j_cmam-2025-0046_ref_006","DOI":"10.1073\/pnas.96.6.2612"},{"unstructured":"P. A. Davidson,\nIntroduction to Magnetohydrodynamics,\nCambridge Texts Appl. 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