Stability and Resonances of Multistep Cosine Methods

Stability and Resonances of Multistep Cosine Methods

Year:    2012

Journal of Computational Mathematics, Vol. 30 (2012), Iss. 5 : pp. 517–532

Abstract

In a previous paper, some particular multistep cosine methods were constructed which proved to be very efficient because of being able to integrate in a stable and explicit way linearly stiff problems of second-order in time. In the present paper, the conditions which guarantee stability for general methods of this type are given, as well as a thorough study of resonances and filtering for symmetric ones (which, in another paper, have been proved to behave very advantageously with respect to conservation of invariants in Hamiltonian wave equations). What is given here is a systematic way to analyse and treat any of the methods of this type in the mentioned aspects.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/jcm.1203-m3487

Journal of Computational Mathematics, Vol. 30 (2012), Iss. 5 : pp. 517–532

Published online:    2012-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    16

Keywords:    Exponential integrators Multistep cosine methods Second-order partial differential equations Stability Resonances.

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