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

Gayaz Khakimzyanov (1) , Denys Dutykh (2)

1 Institute of Computational Technologies
2 LAMA - Laboratoire de Mathématiques

In the present note 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.

Mots clés: finite differences; non-uniform grids; boundary layer; boundary value problems; supraconvergence

Domaines: Mécanique des fluides [physics.class-ph]; Analyse numérique [math.NA]; Analyse classique [math.CA]; Analyse numérique [cs.NA]; Physique Numérique [physics.comp-ph]

Gayaz Khakimzyanov, Denys Dutykh. On supraconvergence phenomenon for second order centered finite differences on non-uniform grids. 2016. ⟨hal-01223522v3⟩