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A Numerical Study of Two Moving Mesh Method for System of One-Dimensional Time-Dependent Partial Diffrential Equations Which are Based on The Equidistribution Principle

Sangaré Boureima, Somé Blaise, Somé Longin


In the past several years, several numerical techniques have been developed to solve time-dependent partial differential equations (PDEs) in one dimension having solutions with steep gradients in space and in time. In 1990's, moving mesh methods came into spotlight of active research when Huang et al. manage to derive continuous moving mesh equations, or better known as the moving mesh partial differential equations (MMPDEs). This papers is devoted to an evaluation and comparison, mainly based on extensive numerical tests, of two methods for 1D problems namely the adaptive moving mesh method of Russell and co-workers and a moving mesh method based on ideas adopted from Dorfi and Drury. Our examination of these two methods is aimed at assessing which is the most suitable from the point of view of retaining the acknowledged features of reliability, robustness and eficiency
of the conventional method of line approach. Considerable attention is paid to the temporal performance of the methods.


Moving mesh, Partial differential equations (PDEs), h-refinement, r-refinement, Denite difference methods (FDMs), method of lines (MOL), monitor functions

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