{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:20:26Z","timestamp":1760242826522,"version":"build-2065373602"},"reference-count":33,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2016,12,15]],"date-time":"2016-12-15T00:00:00Z","timestamp":1481760000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"2013 general project of Educational Commission of Liaoning Province","award":["L2013434"],"award-info":[{"award-number":["L2013434"]}]},{"name":"2014 Dalian university of foreign languages","award":["2014XJQN1"],"award-info":[{"award-number":["2014XJQN1"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"<jats:p>This paper proposes moving mesh strategies for the moving mesh methods when solving the nonlinear time dependent partial differential equations (PDEs). Firstly we analyse Huang\u2019s moving mesh PDEs (MMPDEs) and observe that, after Euler discretion they could be taken as one step of the root searching iteration methods. We improve Huang\u2019s MMPDE by adding one Lagrange speed term. The proposed moving mesh PDE could draw the mesh to equidistribution quickly and stably. The numerical algorithm for the coupled system of the original PDE and the moving mesh equation is proposed and the computational experiments are given to illustrate the validity of the new method.<\/jats:p>","DOI":"10.3390\/a9040086","type":"journal-article","created":{"date-parts":[[2016,12,15]],"date-time":"2016-12-15T10:53:16Z","timestamp":1481799196000},"page":"86","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["Moving Mesh Strategies of Adaptive Methods for Solving Nonlinear Partial Differential Equations"],"prefix":"10.3390","volume":"9","author":[{"given":"Qinjiao","family":"Gao","sequence":"first","affiliation":[{"name":"School of Economics and Management, Dalian University of Foreign Languages, Dalian 116044, China"}]},{"given":"Shenggang","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Public Health, Dalian Medical University, Dalian 116044, China"}]}],"member":"1968","published-online":{"date-parts":[[2016,12,15]]},"reference":[{"key":"ref_1","unstructured":"Meis, T., and Marcowitz, U. 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