Transfer of boundary conditions for

In this paper, the concept of Abramov's method for transferring boundary conditions posed for regular ordinary diierential equations is applied to index 1 DAEs. Having discussed the reduction of inhomogeneous problems to homogeneous ones and analyzed the underlying ideas of Abramov's method, we consider boundary value problems for index 1 linear DAEs both with constant and varying leading matrix. We describe the relations deening the subspaces of solutions satisfying the prescribed boundary conditions at one end of the interval. The index 1 DAEs that realize the transfer are given and their properties are studied. The results are reformulated for inhomogeneous index 1 DAEs, as well. 1 Preliminaries 1.1 Transforming to homogeneous systems In the theory of regular linear ordinary diierential equations, there exist simple tricks that allow to transform inhomogeneous systems into homogeneous ones (of higher dimension) and, at least at the theoretical level, the investigations may be carried out only for homogeneous systems. This approach simpliies the theory. Of course, the new homogeneous system is of a special form. Therefore, when handling inhomogeneous systems, especially when constructing eecient numerical algorithms, these specialities have to be taken into account. Let the boundary value problem be of the following form: