Asymptotic annihilation hermitian algorithm for integration in time

A higher order hermitian finite difference algorithm for step-by-step integration in time possessing asymptotic annihilation attribute is presented. Particular attention is devoted to the order of accuracy (local truncation error and period dispersion) and numerical high frequency dissipation (numerical damping). The computational effort of the algorithm for lumped model is similar to Newmark’s method and it is in competition with other high-order algorithms presented in literature.