Indices and Solvability for General Systems of Differential
Equations
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Reference: Computer Algebra in Scientific Computing -
CASC '99, V.G. Ghanza, E.W. Mayr, E.V. Vorozhtsov (eds.), Springer-Verlag,
Berlin 1999, pp. 365-385 (invited contribution) |
Description: This article continues the work begun in
[14]
on
the application of the formal theory to the numerical analysis of general systems of
differential equations. It shows how the results obtained there can be
extended from ordinary to partial differential equations. Whereas most
index definitions for partial differential equations which can be
found in the literature are based on semi-discretisations or integral
transforms, our definitions are completely intrinsic and thus really
capture structural properties of the systems. Furthermore, they can be
applied to completely arbitrary systems (linear, non-linear, ...). |
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