In this paper, the 2.5-dimensional resistive Magnetohydrodynamics (MHD) equations were solved to simulate two magnetic reconnection problems in single current sheet by applying the space-time Conservation Element and Solution Element (CESE) method. Three different versions of CESE method are employed: (1) the original CESE method, (2) the Courant Number Insensitive Scheme (CNIS) CESE method, (3) the high order CESE method. The numerical results obtained from the above-mentioned approaches are discussed in the aspect of the divergence of the magnetic field. The numerical results indicate that no obvious differences exist among the three approaches in the configuration of the magnetic field. However, for the divergence of the magnetic field, the results obtained from the three approaches differ from each other. In respect to keeping the divergence of the magnetic field small, the CNIS method is better than the others. It is hoped that these conclusions might be helpful for the design of algorithm where the magnetic reconnection problems should be included, since the controlling of the divergence of the magnetic field is one of the key issues in MHD simulation.