Remote Access Mathematics of Computation
Green Open Access

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
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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}})$.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Mathematics of Computation with MSC: 65L05

Retrieve articles in all journals with MSC: 65L05

Additional Information

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

American Mathematical Society