A Novel Single-Step Unconditionally Stable Numerical Integration Scheme With Tunable Algorithmic Dissipation

Abstract

A novel single-step time integration method is proposed for general dynamic problems. From linear spectral analysis, the new method with optimal parameters has second-order accuracy, unconditional stability, controllable algorithmic dissipation and zero-order overshoot in displacement and velocity. Comparison of the proposed method with several representative implicit methods shows that the new method has higher accuracy than the single-step generalized-α method, and also than the composite P∞-Bathe method when mild algorithmic dissipation is used. Besides, this method is spectrally identical to the linear two-step method, although being easier to use since it does not need additional start-up procedures. Its numerical properties are assessed through numerical examples, and the new method shows competitive performance for both linear and nonlinear problems.