On projected Runge-Kutta methods for differential-algebraic equations |
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Authors: | Ch Lubich |
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Institution: | (1) Universität Innsbruck, Institut für Mathematik und Geometrie, Technikerstraße 13, A-6020 Innsbruck, Austria |
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Abstract: | Ascher and Petzold recently introducedprojected Runge-Kutta methods for the numerical solution of semi-explicit differential-algebraic systems of index 2. Here it is shown that such a method can be regarded as the limiting case of a standard application of a Runge-Kutta method with a very small implicit Euler step added to it. This interpretation allows a direct derivation of the order conditions and of superconvergence results for the projected methods from known results for standard Runge-Kutta methods for index-2 differential-algebraic systems, and an extension to linearly implicit differential-algebraic systems. |
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Keywords: | AMS(MOS) 65L05 |
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