In this paper we introduce two moving mesh methods for solving time dependent partial dierential equationsPDEsin divergence form The rst method uses a cell averaging cubic Hermite collocation discretization for the physical PDEs and a three point nite dierence discretization for the PDE which determines the moving mesh The second method is an adaptive mesh redistribution method with two part moving mesh and PDE evolution Numerical result that mention the e ciency of two methods

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