A novel perspective for simulations of the MEW equation by trigonometric cubic B-spline collocation method based on Rubin-Graves type linearization

YAĞMURLU N. M., Karakaş A. S.

Computational Methods for Differential Equations, cilt.10, sa.4, ss.1046-1058, 2022 (ESCI, Scopus) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 10 Sayı: 4
  • Basım Tarihi: 2022
  • Doi Numarası: 10.22034/cmde.2021.47358.1981
  • Dergi Adı: Computational Methods for Differential Equations
  • Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI), Scopus, zbMATH, Directory of Open Access Journals
  • Sayfa Sayıları: ss.1046-1058
  • Anahtar Kelimeler: Collocation method, Finite element method, Modified equal width equation, Solitary waves, Trigonometric B-splines
  • İnönü Üniversitesi Adresli: Evet

Özet

In the present study, the Modified Equal Width (MEW) wave equation is going to be solved numerically by presenting a new technique based on the collocation finite element method in which trigonometric cubic B-splines are used as approximate functions. In order to support the present study, three test problems; namely, the motion of a single solitary wave, the interaction of two solitary waves, and the birth of solitons are studied. The newly obtained results are compared with some of the other published numerical solutions available in the literature. The accuracy of the proposed method is discussed by computing the numerical conserved laws as well as the error norms L2 and L∞.