  In this work, we present three linear numerical schemes to model nematic
liquid crystals using the Landau-de Gennes $\textbf{Q}$-tensor theory. The
first scheme is based on using a truncation procedure of the energy, which
allows for an unconditionally energy stable first order accurate decoupled
scheme. The second scheme uses a modified second order accurate optimal
dissipation algorithm, which gives a second order accurate coupled scheme.
Finally, the third scheme uses a new idea to decouple the unknowns from the
second scheme which allows us to obtain accurate dynamics while improving
computational efficiency. We present several numerical experiments to offer a
comparative study of the accuracy, efficiency and the ability of the numerical
schemes to represent realistic dynamics.
