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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Vydáno v:Iranian journal of numerical analysis and optimization Ročník 15; číslo Issue 2; s. 655 - 675
Hlavní autoři: Y.H. Youssri, A.G. Atta, M.O. Moustafa, Z.Y. Abu Waar
Médium: Journal Article
Jazyk:angličtina
Vydáno: Ferdowsi University of Mashhad 01.06.2025
Témata:
chebyshev polynomials
convergence analysis
nonlinear fractional-order duffing equation
spectral methods
ISSN:2423-6977, 2423-6969
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Popis
Shrnutí: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