Unconditionally Stable Time-Step-Integration Algorithms Based on Hamilton's Principle

Unconditionally stable time-step-integration algorithms derived from Hamilton's principle are presented. The corresponding constrained variations are assumed to be in the form of Σα k τ k (1 - τ) to ensure vanishing variations at the ends of a time interval. The initial conditions are strongly enforced in the formulation. The order of accuracy can be 2n - 1 or 2n, where n is the number of unknown variables. The ultimate spectral radii of the algorithms can be controlled directly, The approximate solutions are in fact equivalent to the generalized Pade approximations for linear second-order differential equations. Hence, Hamilton's principle can be used to construct unconditionally stable higher-order-accurate time-step-integration algorithms directly as well, provided the appropriate constrained variations are used.