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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

A necessary condition for $ A$-stability of multistep multiderivative methods


Author: Rolf Jeltsch
Journal: Math. Comp. 30 (1976), 739-746
MSC: Primary 65L05
MathSciNet review: 0431690
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Abstract: The region of absolute stability of multistep multiderivative methods is studied in a neighborhood of the origin. This leads to a necessary condition for A-stability. For methods where $ \rho (\zeta )/(\zeta - 1)$ has no roots of modulus 1 this condition can be checked very easily. For Hermite interpolatory and Adams type methods a necessary condition for A-stability is found which depends only on the error order and the number of derivatives used at $ ({x_{n + k}},{y_{n + k}})$.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0025-5718-1976-0431690-X
PII: S 0025-5718(1976)0431690-X
Keywords: Linear k-step methods using higher derivatives, behavior of the region of absolute stability at the origin, necessary condition for A-stability, Hermite interpolatory multistep multiderivative methods, Adams-type multistep multiderivative methods
Article copyright: © Copyright 1976 American Mathematical Society