A collocation method for solving time fractional nonlinear Korteweg–de Vries–Burgers equation arising in shallow water waves


Karaagac B., Esen A., Owolabi K. M., Pindza E.

INTERNATIONAL JOURNAL OF MODERN PHYSICS C, cilt.34, sa.07, ss.1-16, 2023 (SCI-Expanded)

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 34 Sayı: 07
  • Basım Tarihi: 2023
  • Doi Numarası: 10.1142/s0129183123500961
  • Dergi Adı: INTERNATIONAL JOURNAL OF MODERN PHYSICS C
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Applied Science & Technology Source, Computer & Applied Sciences, INSPEC, zbMATH
  • Sayfa Sayıları: ss.1-16
  • İnönü Üniversitesi Adresli: Evet

Özet

This paper focuses on numerical solutions of time fractional nonlinear Korteweg–de Vries–Burgers equation formulated with Caputo’s fractional derivative. For this purpose, a framework of combinations of collocation method with the finite-element method is provided using trigonometric quintic B-spline basis. The method consists of both spatial discretization and temporal discretization using approximate solution and Crank–Nicolson approach. Discretizing fractional derivative is made using [Formula: see text] algorithm which is derived from the definition of Caputo derivative using an approximate function. The stability analysis is established using von-Neumann stability technique. The numerical results obtained using the collocation method are presented via tables and graphics. The novel results demonstrate the efficiency and reliability of the method.