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

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...

Full description

Saved in:
Bibliographic Details
Published in:Alexandria engineering journal 2021-12, Vol.60 (6), p.5331-5340
Main Authors: Cinar, Melih, Secer, Aydin, Bayram, Mustafa
Format: Article
Language:English
Subjects:
Collocation method
Fractional calculus
Fractional Rosenau-Hyman equation
Genocchi wavelet
K(n,n) equation
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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.
ISSN:1110-0168
DOI:10.1016/j.aej.2021.04.037