On diagonally iterated Runge-Kutta methods for dissipative ODEs

In this paper, we show that for most classical Runge-Kutta methods, there exist diagonally implicit schemes that are convergent for the class of dissipative problems. For singly implicit methods, it is shown that the iteration of van der Houwen and Sommeijer (1991) is also convergent in this context. However, numerical results indicate that the schemes obtained for the Gauss and Radau IIA methods are far less efficient than those obtained in van der Houwen and Sommeijer (1991).