Conservation of invariants by symmetric multistep cosine methods for second-order partial differential equations

In a previous paper, some multistep cosine methods which integrate exactly the linear and stiff part of a second-order differential equation have been introduced and its convergence has been analysed under assumptions of regularity. In this paper, we characterize when this type of methods are symmetric and give a detailed analysis which allows to prove that these symmetric methods behave very advantageously with respect to the conservation of invariants when a Hamiltonian wave equation subject to periodic boundary conditions is integrated. In this way we prove that these methods are really competitive since they are explicit, stable and qualitatively correct for this type of equations.