1 Scientific Computing, Department of Informatics and Mathematical Modeling, Technical University of Denmark2 Department of Informatics and Mathematical Modeling, Technical University of Denmark3 Department of Applied Mathematics and Computer Science, Technical University of Denmark
The report presents a numerical method for the solution of stiff systems of ODE's and index one DAE's. The type of method is a 4- stage Generalized Linear Method that is reformulated in a special Semi Implicit Runge Kutta Method of SDIRK type. Error estimation is by imbedding a method of order 4 based on the same stages as the method and the coefficients are selected for ease of implementation. The method has 4 stages and the stage-order is 2. For purposes of generating dense output and for initializing the iteration in the internal stages a continuous extension is derived. The method is A-stable and we present the region of absolute stability and the order star of the order 3 method that is used for computing the solution.