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Index and characteristic analysis of linear PDAE systems. (English) Zbl 1036.65081
Summary: Automatable analyses of the index and well-posedness of two general classes of linear partial differential-algebraic equations (PDAEs) are presented for use in equation-based dynamic simulation packages. These analyses determine whether a problem possesses a unique solution trajectory, the potential effect of noise in the initial and boundary conditions on the calculated solution, and the index of the model equations. Measures of the degeneracy of the system, rather than a differentiation index, bound the order of derivatives of forcing functions that appear in the solution.
MSC:
65M70Spectral, collocation and related methods (IVP of PDE)
35R10Partial functional-differential equations