This paper is concerned with discretizing the boundary value problems in ordinary differential equations. We set up a total of 4 schemes for a boundary value problem $x''=f(t,x)$ on $[0,1]$, $R_ix=y_i$ $(i=1,2,)$, with four classes of linear functionals $R_i$ on $C^1[0,1]$ on a nonuniform mesh.