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.Comment: 26 pages, 2 figures, 2 tables, 37 references. Other author's papers
can be downloaded at http://www.denys-dutykh.com