Abstract
This paper examines two families of diagonally implicit methods with s internal and r external stages based on the Nordsieck approach and the multistep Runge–Kutta approach. Two general classes of methods are constructed both with order $r + 1$ and stage order $r - 1$. The A-stability of these methods is studied, and it is shown numerically that there exist A-stable diagonally implicit methods of order up to eight. The stiff order of these methods is investigated numerically, and it appears that the stiff order is equal to the stage order or one more than the stage order.
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