Abstract:The precise time step integration method proposed for

linear time-invariant homogeneous dynamic system can give precise numerical

results approaching to the exact solution at the integration points.

However, it is more or less difficult when the algorithm is used to the

non-homogeneous dynamic systems due to the inverse matrix calculation and

the simulation accuracy of the applied loading. By combining the Gauss

quadrature method and state space theory with the calculation technique of

matrix exponential function in the precise time step integration method, a

new precise time step integration method (that is renewal precise time step

integration method) is proposed. The new method avoids the inverse matrix

calculation and the simulation of the applied loading and improves the

computing efficiency. In particular, the method is independent to the

quality of the matrix ${\pmb H}$. If the matrix ${\pmb H}$ is singular or nearly singular,

the advantage of the method is remarkable. The proposed method in this paper

is a unconditionally stable algorithm having an arbitrary order of accuracy.

Numerical examples are given to demonstrate the validity and efficiency of

the algorithm.