A collocation method for solving time fractional nonlinear Korteweg-de Vries-Burgers equation arising in shallow water waves
Küçük Resim Yok
Tarih
2023
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
World Scientific Publ Co Pte Ltd
Erişim Hakkı
info:eu-repo/semantics/closedAccess
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 L1(0 <= 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.
Açıklama
Anahtar Kelimeler
Korteweg-de Vries-Burgers equation, Caputo fractional derivative, collocation method, trigonometric quintic B-splines, von-Neumann stability technique
Kaynak
International Journal of Modern Physics C
WoS Q Değeri
Q2
Scopus Q Değeri
Q3
Cilt
34
Sayı
7
