Weight Estimates of the Accuracy of Difference Schemes for the Sturm–Liouville Problem

It is shown that the rate of convergence of difference schemes used for the solution of the Sturm–Liouville problem for linear ordinary differential equations is higher in the immediate vicinity of the boundary. Moreover, we obtain the a priori estimates of accuracy that can be regarded as a quantitative confirmation of this effect. The results of numerical experiments corroborating this effect are also presented.