A study of the computational efficiency of two numerical methods based on a mixed finite difference-Galerkin technique is undertaken. This study uses steady Rayleigh-Benard convection in a periodic container as a model problem. The formulation and linearization of the reduced Galerkin and pseudo-spectral methods is discussed. A new technique for reducing the computational effort of evaluating the convolution sums is used. It is found that the reduced Galerkin method allows greater linearization of the equations of fluid motion. Additionally, the reduced Galerkin method is approximately three times faster than the pseudo-spectral method for the problem studied.