Compared with ferromagnetic counterparts, antiferromagnetic materials are considered as the future of spintronic applications since these materials are robust against the magnetic perturbation, produce no stray field, and display ultrafast dynamics. There are (at least) two sets of magnetic moments in antiferromagnets (with magnetization of the same magnitude but antiparallel directions) and ferrimagnets (with magnetization of the different magnitude). The coupled dynamics for the bipartite collinear antiferromagnets is modeled by a coupled system of Landau-Lifshitz-Gilbert equations with an additional term originated from the antiferromagnetic exchange, which leads to femtosecond magnetization dynamics. In this paper, we develop three Gauss-Seidel projection methods for micromagnetics simulation in antiferromagnets and ferrimagnets. They are first-order accurate in time and second-order in space, and only solve linear systems of equations with constant coefficients at each step. Femtosecond dynamics, Néel wall structure, and phase transition in presence of an external magnetic field for antiferromagnets are provided with the femtosecond stepsize.