10.1186/2251-7456-7-25

Petrov-Galerkin finite element method for solving the MRLW equation

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  • Seydi Battal Gazi Karakoc*1,
  • Turabi Geyikli2,
  1. Department of Mathematics, Faculty of Science and Art, Nevsehir University, Nevsehir, 50300, TR
  2. Department of Mathematics, Faculty of Science and Art, Inonu University, Malatya, 44280, TR
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Published in Issue 2013-05-14

How to Cite

Gazi Karakoc, S. B., & Geyikli, T. (2013). Petrov-Galerkin finite element method for solving the MRLW equation. Mathematical Sciences, 7(1). https://doi.org/10.1186/2251-7456-7-25
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Abstract

Abstract Abstract In this article, a Petrov-Galerkin method, in which the element shape functions are cubic and weight functions are quadratic B-splines, is introduced to solve the modified regularized long wave (MRLW) equation. The solitary wave motion, interaction of two and three solitary waves, and development of the Maxwellian initial condition into solitary waves are studied using the proposed method. Accuracy and efficiency of the method are demonstrated by computing the numerical conserved laws and L 2 , L ∞ error norms. The computed results show that the present scheme is a successful numerical technique for solving the MRLW equation. A linear stability analysis based on the Fourier method is also investigated.

Keywords

  • Finite element method,
  • Petrov-Galerkin,
  • MRLW equation,
  • Splines,
  • Solitary waves,
  • MSC 65N30,
  • 65D07,
  • 74S05,
  • 74J35,
  • 76B25
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