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 DUTYKHConnect in order to contact the contributor Submitted on : Sunday, April 9, 2017 - 6:21:15 PM Last modification on : Wednesday, November 3, 2021 - 6:17:37 AM Long-term archiving on: : 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. Journal of Computational and Applied Mathematics, Elsevier, 2017, 326, pp.1-14. ⟨10.1016/j.cam.2017.05.006⟩. ⟨hal-01223522v5⟩