Numerical computing approach for solving Hunter-Saxton equation arising in liquid crystal model through sinc collocation method


Ahmad I., Ilyas H., KUTLU K. , Anam V., Hussain S. I. , Garcia Guirao J. L.

HELIYON, vol.7, no.7, 2021 (Journal Indexed in ESCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 7 Issue: 7
  • Publication Date: 2021
  • Doi Number: 10.1016/j.heliyon.2021.e07600
  • Title of Journal : HELIYON
  • Keywords: Sinc collocation method (SCM), Hunter-Saxton equation (HSE), Liquid crystals (LC), Stability analysis, Numerical solution of PDEs, PARTIAL-DIFFERENTIAL-EQUATIONS, HYBRID METHOD, DYNAMICS, SYSTEM

Abstract

In this study, numerical treatment of liquid crystal model described through Hunter-Saxton equation (HSE) has been presented by sinc collocation technique through theta weighted scheme due to its enormous applications including, defects, phase diagrams, self-assembly, rheology, phase transitions, interfaces, and integrated biological applications in mesophase materials and processes. Sinc functions provide the procedure for function approximation over all types of domains containing singularities, semi-infinite or infinite domains. Sinc functions have been used to reduce HSE into an algebraic system of equations that makes the solution quite superficial. These algebraic equations have been interpreted as matrices. This projected that sinc collocation technique is considerably efficacious on computational ground for higher accuracy and convergence of numerical solutions. Stability analysis of the proposed technique has ensured the accuracy and reliability of the method, moreover, as the stability parameter satisfied the condition the proposed solution of the problem converges. The solution of the HSE is presented through graphical figures and tables for different cases that are constructed on various values of theta and collocation points. The accuracy and efficiency of the proposed technique is analyzed on the basis of absolute errors.