Improved traditional Rosenbrock-Wanner methods for stiff ODEs and DAEs

Rosenbrock–Wanner methods usually have order reduction if they are applied on stiff ordinary differential or differential algebraic equations. Therefore in several papers further order conditions are derived to reduce this effect. In [13] the example of Prothero and Robinson is analysed to find further order conditions. In this paper we consider traditional ROW methods like ROS3P [7], ROS3PL [6], and RODASP [18] and modify these methods such that these further order conditions are satisfied. Numerical examples show the advantages of the new methods.