The Hunter‐Saxton Equation: A Numerical Approach Using Collocation Method

In this study, we are going to present an overview on the Hunter‐Saxton equation which is a famous equation modelling waves in a massive director field of a nematic liquid crystal. The collocation finite element method is based on quintic B‐spline basis for obtaining numerical solutions of the equation. Using this method, after discretization, solution of the equation expressed as linear combination of shape functions and B‐spline basis. So, Hunter‐Saxton equation converted to nonlinear ordinary differential equation system. With the aid of the error norms and , some comparisons are presented between numeric and exact solutions for different step sizes. As a result, the authors observed that the method is a powerful, suitable and reliable numerical method for solving various kind of partial differential equations.