Abstract
Rosenbrock-Wanner methods for solving index-one DAEs usually suffer from order reduction to order p = 1 when the Jacobian matrix is not exactly computed in every time step. This may even happen when the Jacobian matrix is updated in every step, but numerically evaluated by finite differences. Recently, Jax (A rooted-tree based derivation of ROW-type methods with arbitrary jacobian entries for solving index-one DAEs, Dissertation, University Wuppertal (to appear)) could derive new order conditions for the avoidance of such order reduction phenomena. In this paper we present an improvement of the known Rosenbrock-Wanner method rodasp (Steinebach, Order-reduction of ROW-methods for DAEs and method of lines applications, Preprint-Nr. 1741. FB Mathematik, TH Darmstadt (1995)). It is possible to modify its coefficient set such that only an order reduction to p = 2 occurs. Several numerical tests indicate that the new method is more efficient than rodasp and the original method rodas from Hairer and Wanner (Solving Ordinary Differential Equations II, Stiff and differential algebraic Problems, 2nd edn. Springer, Berlin, Heidelberg (1996)). When additionally measures for the efficient evaluation of the Jacobian matrix are applied, the method can compete with the standard integrator ode15s of MATLAB.
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Steinebach, G. (2020). Improvement of Rosenbrock-Wanner Method RODASP. In: Reis, T., Grundel, S., Schöps, S. (eds) Progress in Differential-Algebraic Equations II. Differential-Algebraic Equations Forum. Springer, Cham. https://doi.org/10.1007/978-3-030-53905-4_6
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DOI: https://doi.org/10.1007/978-3-030-53905-4_6
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