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.

Keywords

Bibliographic record

BibTeX Citation

@article{Khakimzyanov2017supraconvergencephenomenon,
  author = {Khakimzyanov, G. and Dutykh, D.},
  title = {On supraconvergence phenomenon for second order centered finite differences on non-uniform grids},
  journal = {J. Comp. Appl. Math.},
  year = {2017},
  volume = {326},
  pages = {1--14},
  doi = {10.1016/j.cam.2017.05.006},
  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.},
  keywords = {finite differences, non-uniform grids, boundary layer, boundary value problems, supraconvergence}
}