Approximation Properties of Solutions to Multipoint Boundary-Value Problems

We consider a broad class of linear boundary-value problems for systems m ordinary differential equations order r known as general problems. Their solutions y : [a, b] → ℂm belong to the Sobolev space $$ {\left({W}_1^r\right)}^m and boundary conditions are given in form By = q, where B: (C(r−1))m ℂrm is an arbitrary continuous operator. For this problem, we prove that its solution can be approximated with accuracy by multipoint boundaryvalue same right-hand sides. These constructed explicitly do not depend on sides problem. these problems, obtain estimates errors normed spaces (C(r−1))m.