Approximation properties of solutions to multipoint boundary-value problems
UDC 517.927 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. Their solutions $y\colon[a,b]\to \mathbb{C}^{m}$ belong to the Sobolev space $(W_1^{r})^m,$ and the boundary conditions...
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| Date: | 2021 |
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| Main Authors: | , , , , , , , |
| Format: | Article |
| Language: | Ukrainian |
| Published: |
Institute of Mathematics, NAS of Ukraine
2021
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/6505 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
| Download file: |  |
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Ukrains’kyi Matematychnyi Zhurnal| Summary: | UDC 517.927
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. 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. 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. These multipoint problems are built explicitly and do not depend on the right-hand sides of the general boundary-value problem. For these problems, we obtain estimates of error of solutions in the normed spaces $(W_1^{r})^m$ and $(C^{(r-1)})^{m}.$
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| DOI: | 10.37863/umzh.v73i3.6505 |