Approximation properties of solutions to multipoint boundary-value problems

  • A. A. Murach Institute of Mathematics, NAS of Ukraine
  • O. B. Pelekhata National Technical University of Ukraine “Igor Sikorsky Kyiv Polytechnic Institute”
  • V. O. Soldatov Institute of Mathematics, NAS of Ukraine https://orcid.org/0000-0001-7496-5524

Abstract

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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Published
11.03.2021
How to Cite
Murach, A. A., O. B. Pelekhata, and V. O. Soldatov. “Approximation Properties of Solutions to Multipoint Boundary-Value Problems”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 73, no. 3, Mar. 2021, pp. 341 -53, doi:10.37863/umzh.v73i3.6505.
Section
Research articles