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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 (AFMs) (with magnetization of the same magnitude but antiparallel directions) and ferrimagnets (with the magnetization of the different magnitude). The coupled dynamics of the bipartite collinear AFMs is modeled by a coupled system of Landau–Lifshitz–Gilbert equations with additional terms originated from the interlattice exchange, which leads to femtosecond magnetization dynamics in AFMs. In this article, we develop three Gauss–Seidel projection methods for micromagnetics simulation in AFMs and ferrimagnets. They are first-order accurate in time and second-order accurate in space, and only solve linear systems of equations with constant coefficients at each step. Femtosecond dynamics, Néel wall structure, and phase transition in the presence of an external magnetic field for AFMs are provided with the femtosecond stepsize. [ABSTRACT FROM AUTHOR]