On the Numerical Analysis of Overdetermined Linear Partial Differential Systems
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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.
KeywordsAlgebraic Equation Computer Algebra Triangular Form Underlying System Multi Index
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