Abstract: | In this paper, we investigate the numerical solution of a model equation u
xx
=
exp(–
) (and several slightly more general problems) when ![isin](/content/n8m778600636611k/xxlarge8712.gif) 1 using the standard central difference scheme on nonuniform grids. In particular, we are interested in the error behaviour in two limiting cases: (i) the total mesh point number N is fixed when the regularization parameter ![isin](/content/n8m778600636611k/xxlarge8712.gif) 0, and (ii) is fixed when N![rarr](/content/n8m778600636611k/xxlarge8594.gif) . Using a formal analysis, we show that a generalized version of a special piecewise uniform mesh 12 and an adaptive grid based on the equidistribution principle share some common features. And the optimal meshes give rates of convergence bounded by |log( )| as ![isin](/content/n8m778600636611k/xxlarge8712.gif) 0 and N is given, which are shown to be sharp by numerical tests. |