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Improved traditional Rosenbrock-Wanner methods for stiff ODEs and DAEs. (English) Zbl 1326.65085
Summary: Rosenbrock-Wanner methods usually have order reduction if they are applied to stiff ordinary differential or differential algebraic equations. Therefore, in several papers further order conditions are derived to reduce this effect. In [the author, J. Comput. Appl. Math. 262, 105–114 (2014; Zbl 1302.65179)] the example of A. Prothero and A. Robinson [Math. Comput. 28, 45–162 (1974; Zbl 0309.65034)] is analysed to find further order conditions. In this paper we consider traditional ROW methods such as ROS3P [J. Lang and J. Verwer, BIT 41, No. 4, 731–738 (2001; Zbl 0996.65099)], ROS3Pw [J. Rang and L. Angermann, BIT 45, No. 4, 761–787 (2005; Zbl 1093.65097)], ROS3PL [J. Lang and D. Teleaga, “Towards a fully space-time adaptive FEM for magnetoquasistatics”, IEEE Trans. Magn. 44, No. 6, 1238–1241 (2008; doi:10.1109/TMAG.2007.914837)], and RODASP [G. Steinebach, “Order-reduction of ROW-methods for DAEs and method of lines applications”, Preprint Nr. 1741. Technische Universität Darmstadt (1995)] and improve these methods such that these further order conditions are satisfied. Numerical examples show the advantages of the new methods.

65L04 Numerical methods for stiff equations
34A09 Implicit ordinary differential equations, differential-algebraic equations
65L80 Numerical methods for differential-algebraic equations
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