High-order symmetric multistep cosine methods

In this paper, a general procedure is given to construct explicit high-order symmetric multistep cosine methods. For these integrators, stability for stiff problems and order of consistency under hypotheses of regularity are justified. We also study when resonances can turn up for the methods suggested and give a simple technique to filter them without losing order of consistency. Particular methods of order eight and ten are explicitly constructed and their high efficiency is numerically shown when integrating Euler–Bernoulli equation.