TY - JOUR
T1 - Stability and Resonances of Multistep Cosine Methods
AU - B. Cano & M.J. Moreta
JO - Journal of Computational Mathematics
VL - 5
SP - 517
EP - 532
PY - 2012
DA - 2012/10
SN - 30
DO - http://doi.org/10.4208/jcm.1203-m3487
UR - https://global-sci.org/intro/article_detail/jcm/8447.html
KW - Exponential integrators, Multistep cosine methods, Second-order partial differential equations, Stability, Resonances.
AB - <p style="text-align: justify;">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.</p>