In this paper,we introduce the properties of Hamiltonian equations,symplectic geometric algorithms and symmetric,Magnus expansion and Neumann expansion methods.

Taking two schemes as example,we study Neumann expansion method.

Aiming at the problem that the rotational response is difficult to measure in structural identification,an approximate algorithm based on Neumann expansion theory is developed for rotational response identification.

When structure performance functions can not be explicitly expressed by random variables and need to be determined by finite element analysis, Neumann series expansion is incorporated into finite element numerical tests in the traditional response surface method.

In this method,the computation time of finite-element numerical tests is effectively shortened by introducing the Neumann series expansion,thus improving the computation efficiency.

Then this paper discusses the solutions of the dispersion functions by Monte Carlo method and compares them with those by the Newton iteration method.

With Monte Carlo method, a group of stochastic variable uniformly distributed over [0,1] were used to simulate the uniform illuminance source and the Lambertion reflection in the inner face of the integrating sphere.

One was based on Monte Carlo method,and the ot.