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Algorithms 2016, 9(4), 86; doi:10.3390/a9040086

Moving Mesh Strategies of Adaptive Methods for Solving Nonlinear Partial Differential Equations

1
School of Economics and Management, Dalian University of Foreign Languages, Dalian 116044, China
2
School of Public Health, Dalian Medical University, Dalian 116044, China
*
Author to whom correspondence should be addressed.
Academic Editor: Alicia Cordero
Received: 9 October 2016 / Revised: 22 November 2016 / Accepted: 9 December 2016 / Published: 15 December 2016
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Abstract

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’s 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’s 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. View Full-Text
Keywords: numerical solution; moving mesh; adaptive method; nonlinear partial differential equation numerical solution; moving mesh; adaptive method; nonlinear partial differential equation
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Gao, Q.; Zhang, S. Moving Mesh Strategies of Adaptive Methods for Solving Nonlinear Partial Differential Equations. Algorithms 2016, 9, 86.

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