论文标题
多点边界值问题的解决方案的近似特性
Approximation properties of solutions to multipoint boundary-value problems
论文作者
论文摘要
我们考虑了$ m $ $ r $的$ m $微分方程的系统的一类线性边界值问题，称为一般边界值问题。他们的解决方案$ y：[a，b] \ to \ mathbb {c}^{m} $属于sobolev space $（w_1^{r} {r}）^m $，边界条件以= q $ by = q $ by = q $ by = q $ where $ b：where $ b：n $ b：{c^{（r-1）}}^{m}^{m math \ t of math \ t of math \ t t octer \ to \ mmath \ c}线性操作员。我们证明，可以通过$（W_1^{r}）^m $在$（W_1^{r}）中的任意精度来近似解决此类问题的解决方案，该解决方案是通过解决相同右侧的多点边界值问题的解决方案。这些多点问题是明确构建的，不取决于一般边界值问题的右侧。对于这些问题，我们获得了在规范空间中的解决方案错误的估计值$（W_1^{r}）^m $和$（c^{（r-1）}）^{m} $。
We consider a wide class of linear boundary-value problems for systems of $m$ ordinary differential equations of order $r$, known as general boundary-value problems. Their solutions $y:[a,b]\to \mathbb{C}^{m}$ belong to the Sobolev space $(W_1^{r})^m$, and the boundary conditions are given in the form $By=q$ where $B:(C^{(r-1)})^{m}\to\mathbb{C}^{rm}$ is an arbitrary continuous linear operator. We prove that a solution to such a problem can be approximated with an arbitrary precision in $(W_1^{r})^m$ 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 errors of solutions in the normed spaces $(W_1^{r})^m$ and $(C^{(r-1)})^{m}$.
