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

V. L. Makarov; M. M. Gural’; M. V. Kutniv

doi:10.1007/s10958-017-3278-7

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

Authors: Makarov V.L.¹, Gural’ M.M.², Kutniv M.V.³^,2
Affiliations:
1. Institute of Mathematics, Ukrainian National Academy of Sciences
2. “L’vivs’ka Politekhnika” National University
3. Rzeszow University of Technology
Issue: Vol 222, No 1 (2017)
Pages: 1-25
Section: Article
URL: https://journals.rcsi.science/1072-3374/article/view/239141
DOI: https://doi.org/10.1007/s10958-017-3278-7
ID: 239141

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Abstract

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.