On supraconvergence phenomenon for second order centered finite differences on non-uniform grids
Numerical Analysis
2020-02-20 v5 Numerical Analysis
Classical Analysis and ODEs
Classical Physics
Computational Physics
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.
Cite
@article{arxiv.1511.02770,
title = {On supraconvergence phenomenon for second order centered finite differences on non-uniform grids},
author = {Gayaz Khakimzyanov and Denys Dutykh},
journal= {arXiv preprint arXiv:1511.02770},
year = {2020}
}
Comments
26 pages, 2 figures, 2 tables, 37 references. Other author's papers can be downloaded at http://www.denys-dutykh.com/