With spherical harmonic function expansion and finite difference discretization,an inversion problem of neutron transport equation is turned to solving effective multiplication factor related to eigenvalue problem.According to characteristics of the matrix,Gerschgorin disk theorem is applied to initial value selection without any physical experience.Rayleigh quotient iteration algorithm is used in solving effective multiplication factor.Third order convergence is achieved without a specific initial value.

The Legendre and adjoint Legendre functions are used to study numerically the steady-state and unsteady, axisymmetric incompressible flow between two concentrically rotating spheres.

The application of spetral finite elment method to well-logging problem is discussed.Using spherical harmonic function expansion and finite element method,Boltzmann transport equation is solved numerically,the convergence of the method is approved.A 3-D software is developed to simulate the neutron logging,and the results are satisfied.

FIDAP software Package is the first genaral software for simulation of incompressible viscous flow by using the finite element method.There are 120000 Fortran senterces in it,A brief introduction is given for its theorical models and algorithm functions,the treatment tricks for implanting FIDAP into a PC computer are given also.