ARK methods up to order five
The properties of almost Runge-Kutta (ARK) methods are investigated and methods with \(s\) (stages in each step) \(=p\) (the order of the method) are derived for all orders up to five. Methods with \(s= p+1\) have also been explored and are represented in the single case \(p= 5\). The author discusses the conditions: a) for an ARK to have a specific order; b) for one of these methods to have linear stability properties exactly as for a classical Runge-Kutta method. Results of numerical experiments with the new methods are presented.
scientific article; zbMATH DE number 1204230