The stability boundaries of difference schemes on nonuniform grids

In this paper we consider the problem of dependence of the stability boundary of difference schemes relately to nonuniform grids. We investigate grids having the nonuniformity only at the ends of segment, i.e. the grids with two and three different mesh sizes. It is shown that there exist nonuniform grids for which the difference schemes have a little more stability reserve than in the case of uniform grids having the same number of nodes.