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Volume 30, Issue 5
Stability and Resonances of Multistep Cosine Methods

B. Cano & M.J. Moreta

DOI: 10.4208/jcm.1203-m3487

J. Comp. Math., 30 (2012), pp. 517-532.

Published online: 2012-10

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  • 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.

  • Keywords

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

  • AMS Subject Headings

35L70, 65M12, 65M99.

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JCM-30-517, author = {}, title = {Stability and Resonances of Multistep Cosine Methods}, journal = {Journal of Computational Mathematics}, year = {2012}, volume = {30}, number = {5}, pages = {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.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.1203-m3487}, url = {http://global-sci.org/intro/article_detail/jcm/8447.html} }
TY - JOUR T1 - Stability and Resonances of Multistep Cosine Methods 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 -

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.

B. Cano & M.J. Moreta. (1970). Stability and Resonances of Multistep Cosine Methods. Journal of Computational Mathematics. 30 (5). 517-532. doi:10.4208/jcm.1203-m3487
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