Indexes and Special Discretization Methods for Linear partial Differential Algebraic Equations |
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Authors: | W Lucht K Strehmel C Eichler-Liebenow |
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Institution: | (1) Institut für Numerische Mathematik, Fachbereich Mathematik und Informatik, Martin-Luther-Universität Halle-Wittenberg, Postfach, DE-06099 Halle, Germany, email: lucht@mail.mathematik.uni-halle.de |
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Abstract: | Linear partial differential algebraic equations (PDAEs) of the form Au
t(t, x) + Bu
xx(t, x) + Cu(t, x) = f(t, x) are studied where at least one of the matrices A, B R
n×n
is singular. For these systems we introduce a uniform differential time index and a differential space index. We show that in contrast to problems with regular matrices A and B the initial conditions and/or boundary conditions for problems with singular matrices A and B have to fulfill certain consistency conditions. Furthermore, two numerical methods for solving PDAEs are considered. In two theorems it is shown that there is a strong dependence of the order of convergence on these indexes. We present examples for the calculation of the order of convergence and give results of numerical calculations for several aspects encountered in the numerical solution of PDAEs. |
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Keywords: | Differential algebraic equations partial differential algebraic equations coupled systems indexes consistency conditions convergence of difference schemes method of lines |
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