  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.
