Operator splitting for numerical solution of the modified Burgers' equation using finite element method

UÇAR Y., YAĞMURLU N. M., CELIKKAYA I.

NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, cilt.35, sa.2, ss.478-492, 2019 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 35 Sayı: 2
  • Basım Tarihi: 2019
  • Doi Numarası: 10.1002/num.22309
  • Dergi Adı: NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.478-492
  • Anahtar Kelimeler: collocation method, cubic B-spline, stability analysis, modified Burgers' equation, finite element method, Strang splitting
  • İnönü Üniversitesi Adresli: Evet

Özet

The aim of this study is to obtain numerical behavior of a one-dimensional modified Burgers' equation using cubic B-spline collocation finite element method after splitting the equation with Strang splitting technique. Moreover, the Ext4 and Ext6 methods based on Strang splitting and derived from extrapolation have also been applied to the equation. To observe how good and effective this technique is, we have used the well-known the error norms L-2 and in the literature and compared them with previous studies. In addition, the von Neumann (Fourier series) method has been applied after the nonlinear term has been linearized to investigate the stability of the method.