The dynamics of a solution of rodlike liquid-crystal line molecules are simulated for the related problems of isotropic-nematic spinodal decomposition and the coarsening of misaligned nematic grains. The Doi diffusion equation for the rod distribution function is coupled with the full Onsager intermolecular potential, discretized by the finite-element method, and integrated forward in time by using a parallel, semi-implicit scheme. The Onsager potential models rod interaction on the scale of a single rod length in order to resolve accurately defects and interfaces in structure. Simulation results show the effects of rotational and translational diffusivity ratios on the mechanisms for alignment and phase separation in spinodal decomposition. As rotational motion is restricted, individual grains become more aligned prior to coalescence events. When rods are restricted to diffusive motion along their axis, the spinodal decomposition process is arrested, and the system will reach a pseudo-steady state featuring misaligned nematic grains. These results mark the first dynamic computation of the Doi diffusion equation for spinodal decomposition in nonhomogeneous rigid-rod systems. Nematic coarsening simulations show the effects of misalignment between neighboring ordered domains on the coarsening time and director field around structured interfaces. Results show that the coarsening time is dependent not only on misalignment between grain directors, but also on the tilt angle of the directors into the interface. (C) 2009 Elsevier B.V. All rights reserved.