@article{Murach_Pelekhata_Soldatov_2021, title={Approximation properties of solutions to multipoint boundary-value problems}, volume={73}, url={https://umj.imath.kiev.ua/index.php/umj/article/view/6505}, DOI={10.37863/umzh.v73i3.6505}, abstractNote={<p>UDC 517.927</p> <p>We consider a wide class of linear boundary-value problems for systems of $m$ ordinary differential equations of order $r$ known as the general boundary-value problems. <br>Their solutions $y\colon[a,b]\to \mathbb{C}^{m}$ belong to the Sobolev space $(W_1^{r})^m,$ and the boundary conditions are given in the form $By=q$ where $B\colon(C^{(r-1)})^{m}\to\mathbb{C}^{rm}$ is an arbitrary continuous linear operator. <br>For such a problem, we prove that its solution can be approximated in $(W_1^{r})^m$ with arbitrary precision by solutions to multipoint boundary-value problems with the same right-hand sides. <br>These multipoint problems are built explicitly and do not depend on the right-hand sides of the general boundary-value problem. <br>For these problems, we obtain estimates of error of solutions in the normed spaces $(W_1^{r})^m$ and $(C^{(r-1)})^{m}.$</p> <p>&nbsp;</p&gt;}, number={3}, journal={Ukrains’kyi Matematychnyi Zhurnal}, author={Murach, A. A. and Pelekhata, O. B. and Soldatov, V. O.}, year={2021}, month={Mar.}, pages={341 - 353} }