Numerical solutions of the MRLW equation by cubic B-spline Galerkin finite element method

Karakoc S. B. G., UÇAR Y., YAGMURLU N. M.

KUWAIT JOURNAL OF SCIENCE, cilt.42, sa.2, ss.141-159, 2015 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 42 Sayı: 2
  • Basım Tarihi: 2015
  • Dergi Adı: KUWAIT JOURNAL OF SCIENCE
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.141-159
  • Anahtar Kelimeler: Cubic B-splines, finite element method, Galerkin, MRLW equation, solitary waves, LONG-WAVE EQUATION, SOLITARY WAVES, MODEL
  • İnönü Üniversitesi Adresli: Evet

Özet

In this paper, a numerical solution of the modified regularized long wave (MRLW) equation has been obtained by a numerical technique based on a lumped Galerkin method using cubic B-spline finite elements. Solitary wave motion, interaction of two and three solitary waves have been studied to validate the proposed method. The three invariants (I-1, I-2, I-3) of the motion have been calculated to determine the conservation properties of the scheme. Error norms L-2 and L-infinity have been used to measure the differences between the exact and numerical solutions. Also, a linear stability analysis of the scheme is proposed.