On the application of finite differences, method of lines and pseudo-spectral methods to smectic-C liquid crystals

Purpose: The purpose of this paper is to derive a dynamic equation for modelling the behaviour of smectic-C liquid crystals under the effect of an electric field. Design/methodology/approach: The model equation is solved using a finite difference approximation, method of lines and pseudo-spectral methods. The solutions are compared for accuracy and efficiency. Comparison is made of the efficiency of finite differences, method of lines and pseudo-spectral methods. Findings: The Fourier pseudo-spectral method is shown to be the most efficient approach. Originality/value: This work is original; a computational comparison of numerical schemes applied to liquid crystals has not been found in the literature.