  For a class of partial differential algebraic equations (PDAEs) of
quasi-linear type which include nonlinear terms of convection type a
possibility to determine a time and spatial index is considered. As a typical
example we investigate an application from plasma physics. Especially we
discuss the numerical solution of initial boundary value problems by means of a
corresponding finite difference splitting procedure which is a modification of
a well known fractional step method coupled with a matrix factorization. The
convergence of the numerical solution towards the exact solution of the
corresponding initial boundary value problem is investigated. Some results of a
numerical solution of the plasma PDAE are given.
