On quasi-linear PDAEs with convection: applications, indices, numerical solution

Authors:
W. Lucht;K. Debrabant
Affiliations:
Martin-Luther-Universität Halle-Wittenberg, Fachberich Mathematik und Informatik, Institut für Numerische Mathematik, Postfach, D-06099 Halle, Germany;Martin-Luther-Universität Halle-Wittenberg, Fachberich Mathematik und Informatik, Institut für Numerische Mathematik, Postfach, D-06099 Halle, Germany
Venue:
Applied Numerical Mathematics
Year:
2002

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Abstract

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.