Fehlerabschätzung für ein Runge-Kutta-Verfahren mit mehrfachen Knoten

Kastlunger-Wanner 2] recently studied Runge-Kutta methods with multiple nodes. Their paper using Taylor-expansion generalized results ofButcher 1]. In this paper we consider a Runge-Kutta method of order four with two double nodes. Inserting appropriate integration formulas we deduce a clearly arranged representation for the truncation error. Moreover one can easily derive the conditions for the coefficients. The obtained error bound has a rather simple form — compared with the error bound for the usual (classical) Runge-Kutta method — and in some cases carries a better result.