document: Quasi stage order conditions for SDIRK methods The stage order condition is a simplifying assumption that reduces the number of order conditions to be fulfilled when designing a Runge-Kutta -LRB- RK -RRB- method . Because a DIRK -LRB- diagonally implicit RK -RRB- method can not have stage order greater than 1 , we introduce quasi stage order conditions and derive some of their properties for DIRKs . We use these conditions to derive a low-order DIRK method with embedded error estimator . Numerical tests with stiff ODEs and DAEs of index 1 and 2 indicate that the method is competitive with other RK methods for low accuracy tolerances
doc_bio_tags: B I I I O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I I O O O O O O O O O O O O O O O O O O O O B I I O B I O O O O O O O O O O O O O O O O O O O O O O O O
extractive_keyphrases: quasi stage order conditions embedded error estimator numerical tests sdirk methods
abstractive_keyphrases: diagonally implicit runge-kutta method differential-algebraic systems