Explicit collocation algorithm for the nonlinear fractional Duffing equation via third-kind Chebyshev polynomials

Herein, we propose an accurate algorithm to approximate the solution of the nonlinear fractional-order Duffing equation (NFDE). The algorithm is based on using shifted Chebyshev polynomials of the third-kind as basis functions and the spectral collocation method as a solver. We study the error analy...

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Bibliographic Details
Published in:	Iranian journal of numerical analysis and optimization Vol. 15; no. Issue 2; pp. 655 - 675
Main Authors:	Y.H. Youssri, A.G. Atta, M.O. Moustafa, Z.Y. Abu Waar
Format:	Journal Article
Language:	English
Published:	Ferdowsi University of Mashhad 01.06.2025
Subjects:	chebyshev polynomials convergence analysis nonlinear fractional-order duffing equation spectral methods
ISSN:	2423-6977, 2423-6969
Online Access:	Get full text
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Summary:	Herein, we propose an accurate algorithm to approximate the solution of the nonlinear fractional-order Duffing equation (NFDE). The algorithm is based on using shifted Chebyshev polynomials of the third-kind as basis functions and the spectral collocation method as a solver. We study the error analysis of the method in-depth, and we exhibit some numerical test problems to check the applicability of the method. Also, we compare it with other existing techniques to show the superiority of our proposed numerical scheme. Our results show that the method employed provides a useful tool to simulate the solution of the NFDE. The main advantages of the proposed method are that it does not require a huge number of retained modes, simply a few terms, and does not exhaust the machine used to render the codes.
ISSN:	2423-6977 2423-6969
DOI:	10.22067/ijnao.2025.90483.1543