On the stability of the Abramov transfer for differential-algebraic equations of index 1

The transfer of boundary conditions for ordinary differential equations developed by Abramov [Zh. Vychisl. Mat. Mat. Fiz., 1 (1961), pp. 542-545] is a stable method for representing the solution spaces of linear boundary value problems. Instead of boundary value problems, matrix-valued initial value problems are solved. When integrating these differential equations, the inner independence of the columns of the solution matrix and, hence, of the solutions of the resulting linear system of equations, remains valid. Balla and Marz have generalized Abramov's transfer for homogenized index-1 differential-algebraic equations [SIAM J. Numer. Anal., 33 (1996), pp. 2318-2332.] In this article, a direct version of the Abramov transfer for inhomogeneous linear index-1 differential-algebraic equations is developed and the numerical stability of this method is proved.