Solution to a Damped Duffing Equation Using He’s Frequency Approach

In this paper, we generalize He’s frequency approach for solving the damped Duffing equation by introducing a time varying amplitude. We also solve this equation by means of the homotopy method and the Lindstedt–Poincaré method. High accurate formulas for approximating the Jacobi elliptic function c...

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Bibliographic Details
Published in:TheScientificWorld 2022, Vol.2022, p.1-10
Main Authors: Salas, Alvaro H. S., Altamirano, Gilder-Cieza, Sánchez-Chero, Manuel
Format: Article
Language:English
Subjects:
Approximation
Chebyshev approximation
Duffing equation
Elliptic functions
Oscillators
Pade approximation
Time varying amplitude
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Summary:In this paper, we generalize He’s frequency approach for solving the damped Duffing equation by introducing a time varying amplitude. We also solve this equation by means of the homotopy method and the Lindstedt–Poincaré method. High accurate formulas for approximating the Jacobi elliptic function cn are formally derived using Chebyshev and Pade approximation techniques.
ISSN:2356-6140
1537-744X
1537-744X
DOI:10.1155/2022/5009722