2020/05/05 by Olena Atlasiuk, Atlasiuk, Olena, Vladimir Mikhailets +1 · 1 citation
Mathematics · Computer Science · #Differential Equations and Boundary Problems #Advanced Mathematical Modeling in Engineering #Numerical methods in inverse problems
paper · pdf · doi:10.48550/arxiv.2005.03494
We consider the most general class of linear inhomogeneous boundary-value problems for systems of ordinary differential equations of an arbitrary order whose solutions and right-hand sides belong to appropriate Sobolev spaces. For parameter-dependent problems from this class, we prove a constructive criterion for their solutions to be continuous in the Sobolev space with respect to the parameter. We also prove a two-sided estimate for the degree of convergence of these solutions to the solution of the nonperturbed problem.