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| In this talk we present the main results we have obtained in the study of symmetric and explicit multistep cosine methods, which are a subtype of what are called \lq exponential integrators'. They integrate the linear and stiff part of a problem in an exact way, which makes it possible to obtain methods which are explicit and stable at the same time for linearly stiff problems.
These methods are efficient numerical solvers when integrating second-order in time partial differential problems subject to periodic boundary conditions, like the nonlinear wave or the beam equation, which have a hamiltonian character. The condition of symmetry allows them to show a good long term behaviour. Besides, we have obtained a systematic way to get high accuracy avoiding instability and resonances. |
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