Stability of a difference scheme for a quasi-linear partial differential algebraic system of equations of index $(k,0)$

A quasi-linear partial differential algebraic system of equations of index $(k,0)$ is considered. A spline collocation difference scheme with a split matrix pencil is constructed to numerically solve a system of this kind. The difference scheme has a high accuracy coinciding with the lowest order of the spline approximating the required function. Results of numerical calculations are given.