Stability and Precision Analysis for Precise Integration Method

The precise integration method, one of the direct integration methods for problems in structural dynamics, was analyzed. Several comments were made regarding to its formulation, numerical stability, computational accuracy and cost. The method is conditionally stable and belongs to the category of explicit time-integration methods. The precise integration method is based on the 2N-type algorithm for computation of exponential matrix. It controls the order N to satisfy the accuracy requirement. Its numerical results have excellent correlation. According to the analytic results, the numerical stability, computational accuracy and cost depend to a large degree on the selection of the parameters, time-division, truncation order and order of 2N-type algorithm. Then the optimal formulation of parameters was given. And several points about the precise integration method were illuminated theoretically. Finally, two numerical examples verified the validity of the stability, precision and the optimal formulation.