On pseudodiagonally optimal Runge-Kutta simple iteration methods for systems of differential-algebraic equations of index 1 (Q5954721)

The paper is focused on special features of the use of implicit Runge-Kutta methods for solving large systems of differential-algebraic equations of index 1. Simple iteration can especially be useful in this case since its computer implementation is straightforward irrespective of the dimension of the problem and the number of stages in the Runge-Kutta method. An approach is proposed that makes it possible to construct Runge-Kutta simple iteration methods that are optimal in a certain sense.