Affiliation:
1. Department of Mathematics Inonu University Malatya Turkey
2. Department of Mathematics Education Adıyaman University Adıyaman Turkey
Abstract
AbstractThe 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 and are reported for numerous time and space discretization values in tables. Graphical representations of the solutions describing motion of wave are presented.
Subject
Applied Mathematics,Computer Science Applications,Mechanical Engineering,Mechanics of Materials,Computational Mechanics
Reference13 articles.
1. SwainS SahooB SinghM.Group invariant solutions and conservation laws of the nonlinear Gardner‐Kawahara equation. arXiv preprint arXiv:2104.01427 2021.
2. Exact travelling wave solutions of the nonlinear Gardner‐Kawahara equation by the standard G′/G$$ \left({G}^{\prime }/G\right) $$‐expansion method;Hussein ZH;J Multidiscip Model Optim,2019
3. Soliton solutions to the fifth-order Korteweg–de Vries equation and their applications to surface and internal water waves
4. Soliton solutions for the fifth-order KdV equation and the Kawahara equation with time-dependent coefficients
5. An effective scheme based on quartic B‐spline for the solution of Gardner equation and Harry Dym equation;Zahra WK;Commun Adv Comput Sci Appl,2016
Cited by
1 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献