In this repository, there is the code used for the work on deriving a comprehensive theory for analyzing the order of convergence for non-standard additive Runge-Kutta (NSARK) methods. In principle, the theory allows to formulate order conditions up to any order, however, to obtain solely solution-dependent conditions more effort is needed. As two examples, the known order conditions for MPRK schemes from Kopect and Meister (2nd Order), Kopecz and Meister (3rd Order) and GeCo methods from Martiradonna et al. were derived and expanded up to order 4.
The computation of the Gröbner bases is in the Maple notebook