On the Construction of Stiffly Accurate and B-Stable Runge-Kutta Methods

. In the solution of stiff ODEs and especially DAEs it is desirable that the method used is stiffly accurate and B-stable. In this paper guidelines for the construction of Runge-Kutta methods with these properties are presented. AMS subject classification: 65L06, 65L20 Key words: Runge-Kutta methods, stiff accuracy, B-stability 1 Introduction It is well known that when solving stiff ODEs and especially DAEs, A-stability and stiff accuracy are desirable, see e.g. [4, Theorem 5.9]. Since for every Astable method there exists an equivalent B-stable one of the same order and with the same stability function and since B-stable methods are stable also when applied to nonlinear problems and thus might perform better than just A-stable ones, see e.g. [3], one might just as well aim for B-stability. This paper addresses some of the problems in constructing such methods on basis of a given L-acceptable stability function. In the following we will initially recall some result on the construct..