Indices and Solvability for General Systems of Differential Equations
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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