A new numerical approach to Gardner Kawahara equation in magneto‐acoustic waves in plasma physics

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 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. Then, von Neumann stability analysis is performed for the numerical scheme obtained using collocation finite element method. 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 ∞ are reported for numerous time and space discretization values in tables.Graphical representations of the solutions describing motion of wave are presented.