Rosenbrock-Wanner method

An extension of semi-implicit Runge-Kutta methods is the Rosenbrock-Wanner method. In this method eq. (10.63) is replaced by the expression... 

Coefficients for a fourth-order Rosenbrock-Wanner method are given below ... 

Kaps, P. and Wanner, G., A study of Rosenbrock-type methods of high order, Numer. Math., 38, 279-298,1981. 

Systems 3.1 and 3.2 contain N number of equations. The algebraic equation system can be solved with the Newton-Raphson method [1] and the ordinary differential equations with the semi-implicit Runge-Kutta method, Michelen s semi-implicit Runge-Kutta method [2], or, alternatively, with the Rosenbrock-Wanner semi-implicit Runge-Kutta method [2],... 

M72 Solution of stiff differential equations semi-implicit Runge-Kutta method with backsteps Rosenbrock-Gottwa1d-Wanner 7200 7416... 

For our chemical problem, we successfully use the stiff versions of the solvers LSODE (from A.C.Hindmarsh) and VODE (from G.D.Byrne and A.C.Hindmarsh), which employ multistep methods (backward differentiation formulas) and allow to change stepsize and order of the methods. Comparing investigations show that the IVP-solver RODAS (from E.Hairer and G.Wanner), an implementation of onestep methods (Rosenbrock methods), also with variable stepsize, is working with same success (see e.g. [4, 5]). 

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