And three methods in solving practicable range of Green function are discussed including electric image method,series method and conformal transformation method.

The prediction of the PIM amplitude and power by using the power series method;

The natural frequencies and critical flow velocities of Timoshenko pipe are calculated by power series method.

Based on the Hamilton s principle for elastic systems of changing mass, a differential equation of motion for viscoelastic curved pipes conveying fluid was derived using variational method, and the complex characteristic equation for the viscoelastic circular pipe conveying fluid was obtained by normalized power series method.

Lie series algorithms and Runge-Kutta algorithms;

The three-series solution is taken up to the nonlinear differential equation of the galloping movement caused by the cross wind force acting on a high-rise structure, thus giving a reduced 3D expression in terms of steady-state response and critical wind speed.

An implicit Taylor series method for simulation of power system transient;

Based on the fast higher order Taylor series method for transient stability simulation and combined with the trapezoidal rule of implicit integration, an implicit Taylor series method for transient stability simulation is received.

Since the higher-order Taylor series method was introduced for power system stability, the research of transient stability simulation using the Taylor series method was never interrupted.

In this paper,nonlinearity characteristics and its classification in communication systemsare expatiated,In following discussion,response-characteristics of nonlinearity and its effection arequantificationally described and analysed by Volterra-series.