A Generalized Runge-Kutta Method of order three

We present a numerical method for the solution of sti 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 coe cients 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 delivering the solution.