Symplectic integrators for second-order linear non-autonomous equations

[EN] Two families of symplectic methods specially designed for second-order time-dependent linear systems are presented. Both are obtained from the Magnus expansion of the corresponding first-order equation, but otherwise they differ in significant aspects. The first family is addressed to problems with low to moderate dimension, whereas the second is more appropriate when the dimension is large, in particular when the system corresponds to a linear wave equation previously discretised in space. Several numerical experiments illustrate the main features of the new schemes. (C) 2017 Elsevier B.V. All rights reserved. Bader, Blanes, Casas and Kopylov acknowledge the Ministerio de Economia y Competitividad (Spain) for financial support through the coordinated project MTM2013-46553-C3-3-P. Additionally, Kopylov has been partly supported by fellowship GRISOLIA/2015/A/137 from the Generalitat Valenciana. Bader, P.; Blanes Zamora, S.; Casas, F.; Kopylov, N.; Ponsoda Miralles, E. (2018). Symplectic integrators for second-order linear non-autonomous equations. Journal of Computational and Applied Mathematics. 330:909-919. https://doi.org/10.1016/j.cam.2017.03.028