Dada, Kim2009-05-212009-05-212009-05-21http://hdl.handle.net/10539/6960Abstract In this dissertation both smectic-A and smectic-C liquid crystals are discussed. A dynamic equation for modeling the behaviour of smectic-C liquid crystals under the effect of an electric field is derived. The analytical solution is obtained using Lie point symmetries. From this the steady-state solution is obtained. The model equation is solved using a finite difference approximation, the method of lines and pseudo-spectral methods. The solutions are compared for accuracy and efficiency.enThesis