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On supraconvergence phenomenon for second order centered finite differences on non-uniform grids

Abstract : In the present study we consider an example of a boundary value problem for a simple second order ordinary differential equation, which may exhibit a boundary layer phenomenon. We show that usual central finite differences, which are second order accurate on a uniform grid, can be substantially upgraded to the fourth order by a suitable choice of the underlying non-uniform grid. This example is quite pedagogical and may give some ideas for more complex problems.
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Gayaz Khakimzyanov, Denys Dutykh. On supraconvergence phenomenon for second order centered finite differences on non-uniform grids. Journal of Computational and Applied Mathematics, Elsevier, 2017, 326, pp.1-14. ⟨10.1016/j.cam.2017.05.006⟩. ⟨hal-01223522v5⟩

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