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.
https://hal.archives-ouvertes.fr/hal-01223522
Contributor : Denys Dutykh
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Submitted on : Sunday, April 9, 2017 - 6:21:15 PM
Last modification on : Thursday, January 11, 2018 - 6:12:26 AM
Document(s) archivé(s) le : Monday, July 10, 2017 - 12:10:19 PM
Gayaz Khakimzyanov, Denys Dutykh. On supraconvergence phenomenon for second order centered finite differences on non-uniform grids. 2017. ⟨hal-01223522v5⟩
