Description of helicopter rotor aeroelasticity is essentially a set of stiff and nonlinear partial differential equations. They can be rewritten as non-homogeneous ordinary differential equations after discretion by finite element method. The non-homogeneous terms depend on time response and aerodynamic loads of the blade. This paper introduces precise time integration method (PTI) and its derived formats to solve this kind of equations. As in derived formats, Duhamel integration term in PTI can be calculated using numerical method. It also selects and compares the precise-Kutta method and high precision direct scheme (HPD) on integration precision and numerical stability. At last, implicit integration method is involved to comprehensively review PTI on rotor dynamics. Numerical examples indicate that HPD scheme is precise enough to be used for rectangular blades.