The time evolution of Liquid crystalline configurations quenched suddenly from an isotropic state to a nematic state is simulated using the Monte Carlo method. In the Metropolis sampling procedure, we have employed the Frank free energy involving the splay, bend, and twist elastic constants, surface anchoring energy, and external aligning fields. In the nondiffusive regime, we have derived a scaling law for the defect density rho(t) in terms of time t after quench in space dimension d as rho(t) similar to t(-nu) with nu = d(d + 1)/(d(2) + 2d - 1), which is a generalization of a previous scaling argument in two dimensions. Our simulation results are in agreement with this value of nu in both two and three dimensions. While surface anchoring tends to slow down the kinetics of defect annihilation, elastic anisotropy is found to exert no effect on the value of nu in two dimensions. In the presence of external aligning fields, rho(t) is found to decay exponentially with t.