[en] The mathematical formulation for operation and reactor core fuel management was studied. Using time discrimination, the eigenvalue problem of neutron diffusion equations are governed by reactivity gain in the reactor. From the distribution of neutron flux, power and irradiation, the regulating critical state and fuel management can be described as inverse problem of mathematical physics. The computing simulation of above full procedure was also provided. In addition, a finite element method with proposal accelerating convergence method to eigenvalue problem of neutron diffusion equations was used. The computing time is saved greatly and the convergence speed is much faster compared with other codes for same kind of benchmark problem in the world