Abstract
This paper surveys some stability results and suggests the use of ‘order arrows’ as an alternative to order stars in studying questions about the possible A-stability of a numerical method. A discussion of the so-called Butcher–Chipman conjecture includes a proof of a partial result.
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References
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Butcher, J. The A-Stability of Methods with Padé and Generalized Padé Stability Functions. Numerical Algorithms 31, 47–58 (2002). https://doi.org/10.1023/A:1021155922184
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DOI: https://doi.org/10.1023/A:1021155922184