A Generalized Runge-Kutta Method of order three | Per Grove Thomsen
| | 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. | | Keywords | ODE's , GERK, Stiff systems, Stability, implementation, PI-control | | Type | Technical report | | Year | 2002 Month May No. 07 pp. 14 | | Publisher | IMM, DTU | | Electronic version(s) | [pdf] | | BibTeX data | [bibtex] | | IMM Group(s) | Scientific Computing |
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