An example using the Wilson-θ formula, a precise integration Cotes formula and a precise integration oscillating function integration formula illustrated the high efficiency and accuracy of the precise direct integration method.

In view of the Newmark-precision direct integral method,integration formulas of the non-homogeneous vector are discussed and the stability of this method is analyzed.

Element free-precise integration method for wave equation;

Precise integration for dynamic modeling of water distribution systems;

Instantaneous optimal control algorithm based on precise integration;

A precise integration method for bridges subjected to moving loads;

Wavelet precise integration method for 2D partial differential equations in polygon domain;

Solving time-varying periodic coefficient Riccati differential equations via Fourier series and precise integration method

Spline precise time-integration of structural dynamic analysis

A new precise time-integration method is introduced into the analysis of time domain response to closed-loop switched power converters, which adopts iterative method to obtain exponent matrix, and transformed piecewise linear networks into discrete equations by using quadratic extrapolation on determining the switching instant.

The precise time-integration method was proposed for linear time-invariant dynamic system.

The precise time integration (PTI) proposed for transient linear system can give almost accurate numerical results at the integration point.

Precise time integration is used in the integration of initial value problem, and has been developed, in LQ control problem, to solve TPBV and Riccati matrix differential equation.