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

Abstract

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.

Citation

Dada, K.B. and Momoniat, E. (2010), "On the application of finite differences, method of lines and pseudo‐spectral methods to smectic‐C liquid crystals", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 20 No. 4, pp. 429-444. https://doi.org/10.1108/09615531011035820