A Moving Collocation Method for Solving
نویسندگان
چکیده
A new moving mesh method is introduced for solving time dependent partial diierential equations (PDEs) in divergence form. The method uses a cell-averaging cubic Hermite collocation discretization for the physical PDEs and a three point nite diierence discretization for the PDE which determines the moving mesh. Numerical results are presented for a selection of diicult benchmark problems, including Burgers' equation and Sod's shocktube problem. They indicate third order convergence for the method, slower than the traditional (fourth order) cubic Hermite collocation on a xed mesh but much faster than the rst order of the commonly used moving nite diierence methods. Numerical experiments also show that, in comparison with nite diierences and xed mesh collocation, moving collocation produces more accurate results for small and moderate numbers of mesh points.
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