On the stability of a locally one-dimensional difference scheme for a first-order linear differential-algebraic system of index $(1,0)$

The paper considers an initial-boundary value problem for a linear multidimensional first-order differential-algebraic system of index $(1,0)$. For its numerical solution, a four-point three-layer locally one-dimensional difference scheme is used. It is proved that under certain conditions on the steps of the difference grid, such a scheme is stable in terms of the initial-boundary conditions and in the right-hand side. The results of numerical experiments are presented.