A method for solving linear differential-algebraic systems of equations supplemented with nonlocal conditions specified by the Stieltjes integral

摘要

A method is proposed for solving linear differential-algebraic systems of equations supplemented with nonlocal conditions specified by the Stieltjes integral. The method is based on a series of successive transformations of the original system. The result is either a normal system of differential equations or a system of algebraic equations. In the first case, the use of the supplementary nonlocal condition is realized through the introduction of auxiliary boundary conditions of a standard type.