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

Third Author's Department

Physics Department

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https://doi.org/10.22067/ijnao.2025.90483.1543

All Authors

Youssri Hassan Youssri Ahmed Gamal Atta Mohamed Orabi Moustafa Ziad Yousef Abu Waar

Document Type

Research Article

Publication Title

Iranian Journal of Numerical Analysis and Optimization

Publication Date

1-1-2025

doi

10.22067/ijnao.2025.90483.1543

Abstract

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.

First Page

655

Last Page

675

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