A Generalized Runge-Kutta Method of order three

Per Grove Thomsen

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    Abstract

    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.
    Original languageEnglish
    Publication statusPublished - 2002

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