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

Berat Karaagac, Alaattin Esen (), Kolade M. Owolabi () and Edson Pindza
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Berat Karaagac: Department of Mathematics Education, Adıyaman University, Adıyaman, Turkey
Alaattin Esen: Department of Mathematics, Inonu University, Malatya, Turkey
Kolade M. Owolabi: Department of Mathematical Sciences, Federal University of Technology, Akure, Ondo State, Nigeria
Edson Pindza: Department of Mathematics and Applied Mathematics, University of Pretoria, Pretoria 002, South Africa5Department of Mathematics and Statistics, Tshwane University of Technology, Pretoria West, Pretoria 0183, South Africa

International Journal of Modern Physics C (IJMPC), 2023, vol. 34, issue 07, 1-16

Abstract: 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 L1(0<γ≤1) 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.

Keywords: Korteweg–de Vries–Burgers equation; Caputo fractional derivative; collocation method; trigonometric quintic B-splines; von-Neumann stability technique (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1142/S0129183123500961

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