An application of Genocchi wavelets for solving the fractional Rosenau-Hyman equation


Çınar M. , Seçer A. , Bayram M.

ALEXANDRIA ENGINEERING JOURNAL, cilt.60, sa.6, ss.5331-5340, 2021 (SCI Expanded İndekslerine Giren Dergi)

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 60 Konu: 6
  • Basım Tarihi: 2021
  • Doi Numarası: 10.1016/j.aej.2021.04.037
  • Dergi Adı: ALEXANDRIA ENGINEERING JOURNAL
  • Sayfa Sayıları: ss.5331-5340

Özet

In this research, Genocchi wavelets method, a quite new type of wavelet-like basis, is adopted to obtain a numerical solution for the classical and time-fractional Rosenau-Hyman or K(n,n) equation arising in the formation of patterns in liquid drops. The considered partial differential equation can be transformed into a system of non-linear algebraic equations by utilizing the wavelets method including an integral operational matrix and then discretizing the equation at the collocation points. The system can be simply solved by several traditional methods. Finally, the algorithm is implemented for some numerical examples and the numerical solutions are compared with the exact solutions using MAPLE. The obtained results are demonstrated using figures and tables. When the results are compared, it is evinced that the algorithm is quite effective and advantageous due to its easily computable algorithm, high accuracy, and less process time.