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

KARAAĞAÇ B., ESEN A.

NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, cilt.34, sa.5, ss.1637-1644, 2018 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 34 Sayı: 5
  • Basım Tarihi: 2018
  • Doi Numarası: 10.1002/num.22199
  • Dergi Adı: NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.1637-1644
  • Anahtar Kelimeler: finite element method, collocation method, Hunter-Saxton equation, quintic B-spline
  • İnönü Üniversitesi Adresli: Evet

Özet

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 L-2 and L-infinity, 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.