# Order stars and stability theorems

@article{Wanner1978OrderSA,
title={Order stars and stability theorems},
author={Gerhard Wanner and Ernst Hairer and Syvert P. N{\o}rsett},
journal={BIT Numerical Mathematics},
year={1978},
volume={18},
pages={475-489}
}
• Published 1 December 1978
• Mathematics
• BIT Numerical Mathematics
AbstractThis paper clears up to the following three conjectures:1.The conjecture of Ehle [1] on theA-acceptability of Padé approximations toez, which is true;2.The conjecture of Nørsett [5] on the zeros of the “E-polynomial”, which is false;3.The conjecture of Daniel and Moore [2] on the highest attainable order of certainA-stable multistep methods, which is true, generalizing the well-known Theorem of Dahlquist. We further give necessary as well as sufficient conditions forA-stable (acceptable…
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