Stability inequalities for discrete nonlinear two-point boundary value problems

Abstract

For discretizations of nonlinear two-point boundary value problems we prove estimates of the difference quotients up to order n^-1 in the discrete L_∞-norm by the discrete L₁ -norm of the discretization. In the hierarchy of L_Þ -norms these estimates are best possible. For the linear case deep results P of Grigorieff and Kreiss are generalized.