THERMAL SCIENCE

International Scientific Journal

Shakeel Mehnaz

,

Muhammad Nawaz Khan

,

Imtiaz Ahmad

,

Sayed Abdel-Khalek

,

Ahmed Mohammed Alghamdi

,

Mustafa Inc

THE GENERALIZED TIME FRACTIONAL GARDNER EQUATION VIA NUMERICAL MESHLESS COLLOCATION METHOD

ABSTRACT
In this study, the meshless collocation approach is used to determine the numerical solution the generalized time-fractional Gardner equation. The Crank-Nicolson technique is used to approximate space derivatives, whereas the Caputo derivative of fractional order is used to approximate the first order time fractional derivative. The numerical solutions, which show the method's efficacy and accuracy, are pro­vided and discussed. The numerical solution shows that our method is effective in producing extremely accurate results.
KEYWORDS
time-fractional Gardner equation, Crank-Nicolson scheme, radial basis functions, caputo fractional derivative
PAPER SUBMITTED: 2022-09-12
PAPER REVISED: 2022-11-03
PAPER ACCEPTED: 2022-11-14
PUBLISHED ONLINE: 2023-01-21
DOI REFERENCE: https://doi.org/10.2298/TSCI22S1469M
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2022, VOLUME 26, ISSUE Special issue 1, PAGES [469 - 474]
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The generalized time fractional Gardner equation via numerical meshless collocation method

© 2024 Society of Thermal Engineers of Serbia. Published by the Vinča Institute of Nuclear Sciences, National Institute of the Republic of Serbia, Belgrade, Serbia. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International licence