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2 results on '"Melih Cinar"'

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

Author

Melih Cinar, Aydin Secer, and Mustafa Bayram

Subjects
Fractional Rosenau-Hyman equation, K(n,n) equation, Genocchi wavelet, Collocation method, Fractional calculus, Engineering (General). Civil engineering (General), TA1-2040
Abstract

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.

Published
2021
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2. An application of Genocchi wavelets for solving the fractional Rosenau-Hyman equation☆

Author

Aydin Secer, Mustafa Bayram, Melih Cinar, and Mühendislik ve Doğa Bilimleri Fakültesi

Subjects
Discretization, 020209 energy, 02 engineering and technology, Type (model theory), engineering.material, 01 natural sciences, 010305 fluids & plasmas, Wavelet, 0103 physical sciences, 0202 electrical engineering, electronic engineering, information engineering, Applied mathematics, Collocation method, Mathematics, Maple, Partial differential equation, Collocation, Basis (linear algebra), General Engineering, Fractional calculus, Genocchi wavelet, Engineering (General). Civil engineering (General), Algebraic equation, engineering, K(n,n) equation, Fractional Rosenau-Hyman equation, Fractional Rosenau-Hyman, TA1-2040
Abstract

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. (C) 2021 THE AUTHORS. Published by Elsevier BV on behalf of Faculty of Engineering, Alexandria University.

Published
2021

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