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. (C) 2002 IMACS. Published by Elsevier Science B.V. All rights reserved.