NUMERICAL APPROXIMATION OF HUNTER-SAXTON EQUATION BY AN EFFICIENT ACCURATE APPROACH ON LONG TIME DOMAINS

This paper aimed to propose a combined effective technique for obtaining an approximate solution to the Hunter-Saxton equation arising in the modelling of the direct field of a nematic liquid crystal. The time-marching algorithm is based on the linearized Taylor expansion series while a collocation method based on novel Bessel polynomials is utilized for the space variable. The main advantage of this method is that, in each time step, it converts the problem into a fundamental matrix equation so that the computation is effective and straightforward. Through numerical simulations, the efficiency of the combined scheme is compared with exact solutions as well as existing available numerical models. The results of comparisons indicate that the combined method developed by a large time step and over a large time domain is an efficient approach.