On convergence and approximation of solutions of boundary value problems for quasidifferential equations

Abstract

The paper studies the convergence and approximation of solutions of two-point boundary value problems for the Shin--Zettl quasidifferential equations of arbitrary order $m\in\mathbb{N}$ on the finite interval. The sufficient conditions for the uniform convergence of these solutions are found in terms of coefficient matrices, right-hand members and matrices defining boundary conditions. Also we prove that these solutions may be approximated with solutions of boundary value problems for differential equations with infinitely smooth coefficients.