A Generalized Runge-Kutta Method of order three

Per Grove Thomsen

AbstractThe 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.
KeywordsODE's , GERK, Stiff systems, Stability, implementation, PI-control
TypeTechnical report
Year2002    Month May    No. 07    pp. 14
PublisherIMM, DTU
Electronic version(s)[pdf]
BibTeX data [bibtex]
IMM Group(s)Scientific Computing