Date: 24 Jun 2003

On the Numerical Analysis of Overdetermined Linear Partial Differential Systems

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Abstract

We discuss the use of the formal theory of differential equations in the numerical analysis of general systems of partial differential equations. This theory provides us with a very powerful and natural framework for generalising many ideas from differential algebraic equations to partial differential equations. We study in particular the existence and uniqueness of (formal) solutions, the method of an underlying system, various index concepts and the effect of semi-discretisations.

Supported by Deutsche Forschungsgemeinschaft, Landesgraduiertenförderung Baden-Württemberg and INTAS grant 99-1222.