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A New Numerical Approach to Gardner Kawahara Equation in Magneto-Acoustic Waves in Plasma Physics
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  • berat karaagac,
  • Yusuf UCAR,
  • Nuri YAGMURLU,
  • Alaattin Esen
berat karaagac
Adiyaman Universitesi

Corresponding Author:[email protected]

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Yusuf UCAR
Inonu University
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Nuri YAGMURLU
Inonu Universitesi
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Alaattin Esen
Inonu University
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Abstract

The basic idea of this article is to investigate the numerical solutions of Gardner Kawahara equation, a particular case of extended Korteweg-de Vries (KdV) equation, by means of finite element method. For this purpose, a collocation finite element method based on trigonometric quintic B-spline basis functions is presented. The standard finite difference method is used to discretize time derivative and Crank-Nicolson approach is used to obtain more accurate numerical results. Several numerical examples are presented and discussed to exhibit the feasibility and capability of the finite element method and trigonometric B-spline basis functions. More specifically, the error norms $L_{2}$ and $L_{\infty }$ are reported for numerous time and space discretization numbers in tables. Graphical representations of the solutions which describe motion of wave are presented.