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, ss.478-492, 2019 (SCI İndekslerine Giren Dergi) identifier identifier

  • Cilt numarası: 35 Konu: 2
  • Basım Tarihi: 2019
  • Doi Numarası: 10.1002/num.22309
  • Dergi Adı: NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS
  • Sayfa Sayıları: ss.478-492

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.