Summary.
A new interpretation of Runge-Kutta methods for differential algebraic equations (DAEs) of index 2 is presented, where a step of the method is described in terms of a smooth map (smooth also with respect to the stepsize). This leads to a better understanding of the convergence behavior of Runge-Kutta methods that are not stiffly accurate. In particular, our new framework allows for the unified study of two order-improving techniques for symmetric Runge-Kutta methods (namely post-projection and symmetric projection) specially suited for solving reversible index-2 DAEs.
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Mathematics Subject Classification (1991): 65L05, 65L06
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Chan, R., Chartier, P. & Murua, A. Reversible methods of Runge-Kutta type for Index-2 DAEs. Numer. Math. 97, 427–440 (2004). https://doi.org/10.1007/s00211-003-0499-0
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DOI: https://doi.org/10.1007/s00211-003-0499-0