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.
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O. C. Zienkiewicz (1977) studied this question.