Dynamics of modified improved Boussinesq equation via Galerkin Finite Element Method

Karaagac B., UÇAR Y., ESEN A.

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, cilt.43, sa.17, ss.10204-10220, 2020 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 43 Sayı: 17
  • Basım Tarihi: 2020
  • Doi Numarası: 10.1002/mma.6687
  • Dergi Adı: MATHEMATICAL METHODS IN THE APPLIED SCIENCES
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Applied Science & Technology Source, Communication Abstracts, Compendex, INSPEC, MathSciNet, Metadex, zbMATH, Civil Engineering Abstracts
  • Sayfa Sayıları: ss.10204-10220
  • Anahtar Kelimeler: finite element method, interaction, Lumped Galerkin method, modified improved Boussinesq equation, quadratic B-spline, solitary waves, RELATION PRESERVING METHOD, NUMERICAL-SOLUTIONS, DISPERSION, NONLINEARITIES, SOLITONS, MODEL
  • İnönü Üniversitesi Adresli: Evet

Özet

The aim of this paper is to investigate numerical solutions of modified improved Boussinesq (MIBq) equationutt=uxx+alpha mml:mfenced close=")" open="(" separators=""u3xx+uxxtt, which is a modified type of Boussinesq equations born as an art of modelling water-wave problems in weakly dispersive medium such as surface waves in shallow waters or ion acoustic waves. For this purpose, Lumped Galerkin finite element (LGFE) method, an effective, accurate, and cost-effective method, is applied to model equation by the aid of quadratic B-spline basis. The efficiency and accuracy of the method are tested with two problems, namely, propagation solitary wave and interaction of two solitary waves. The error normsL(2)andL(infinity)have been computed in order to measure how "accurate" the numerical solutions. Also, the stability analysis has been investigated.