Since the presence of a out coupling hole alters the transverse structure of the intra cavity light in a FEL oscillator,the finite element method is used to the optical field equations and a good proximation is made for the out-coupling process in the mirror,and then some numerical results are given.It is shown that the features of the transverse structure of the intra-cavity field are well described and the numerical results are significantly improved.

In this paper, for a class of nonlinear system of equations #br#F₁x₁,x₂=0#br#F₂x₁,x₂=0#br# we formulate a partial Broyden method. The basic idea is that the relation of x₁ to x₂ is determined by the first subsystem of equations F₁=0, then the Broyden method is applied to the second one F₂=0, thus forming a iterative procedure.The application of partical Broyden method to discretized fpT equations is described and numerical results is given.