A new look at the newmark, houbolt and other time stepping formulas. A weighted residual approach

The Newmark time stepping algorithm which was introduced in 1959, using constants γ and β which average the integration process, can be rederived as the most general finite element-weighted residual algorithm involving three consecutive sets of displacements. This derivation is much simpler than that involved originally in the New-mark presentation, and indicates a very wide range of possibilities of approximation. The application of the process to four point (cubic) algorithms leads to another family of formulas of which the Houbolt algorithm is a particular case. The use of the generalized expressions in the context of first-order equations is indicated and shows how some new, as well as some of the old, formulas can be developed.