The Z-transform and linear multistep stability |
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Authors: | Coughlan James J; Hill Adrian T; Logemann Hartmut |
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Institution: |
Department of Mathematical Sciences, University of Bath, Bath BA2 7AY, UK
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Abstract: | ** Email: mapjjc{at}maths.bath.ac.uk*** Corresponding author. Email: ath{at}maths.bath.ac.uk**** Email: hl{at}maths.bath.ac.uk
This paper makes systematic use of control-theoretic methodssuch as the -transform, small-gain theorems and frequency-domainstability criteria in the analysis of the stability behaviourof linear multistep methods. Some of the results in Nevanlinna'swork are recovered and a number of new boundedness and asymptoticproperties of solutions of numerical schemes are obtained. Inparticular, we give a careful and detailed analysis of the nonlinearstability properties of strictly zero-stable methods. |
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Keywords: | behaviour at infinity control theory linear multistep methods nonlinear stability -transform" target="_blank">gif" ALT="Z" BORDER="0">-transform |
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