Enhanced numerical resolution of the Duffing and Van der Pol equations via the spectral homotopy analysis method employing chebyshev polynomials of the first kind

In our investigation, we apply the spectral homotopy analysis method (SHAM) to tackle the numerical resolution of the Duffing and Van Der Pol equations. We compute the numerical solution using Chebyshev polynomials of the first kind as our foundational framework. We optimize the computation of derivative matrices by employing Gauss–Lobatto collocation points. To underscore the practicality and efficiency of our proposed SHAM, we validate our numerical solution against the exact solution and present the error behavior. Furthermore, we demonstrate the superior efficacy of our approach, supported by suitable graphical representations and tables.