This paper presents a novel numerical method, the ultraspherical wavelets collocation method (UWM), for solving the Benjamin-Bona-Mahony (BBM) equation. The method uses ultraspherical wavelets and the collocation technique to approximate solutions of linear and nonlinear BBM equations. The UWM is compared with other numerical methods, including the Haar wavelet method and finite difference method, in terms of accuracy and efficiency. The method is found to be simple, accurate, fast, and flexible, with results validated through tables and graphs. The convergence of the UWM is analyzed, and the method is shown to converge uniformly to the exact solution. The UWM is applied to three different BBM equations, including a linear, non-homogeneous, and nonlinear case. The results demonstrate that the UWM provides more accurate solutions compared to other methods, especially when the parameter M is increased. The method is efficient and suitable for solving both linear and nonlinear BBM equations. The study concludes that the UWM is a promising approach for solving partial differential equations, particularly the BBM equation.This paper presents a novel numerical method, the ultraspherical wavelets collocation method (UWM), for solving the Benjamin-Bona-Mahony (BBM) equation. The method uses ultraspherical wavelets and the collocation technique to approximate solutions of linear and nonlinear BBM equations. The UWM is compared with other numerical methods, including the Haar wavelet method and finite difference method, in terms of accuracy and efficiency. The method is found to be simple, accurate, fast, and flexible, with results validated through tables and graphs. The convergence of the UWM is analyzed, and the method is shown to converge uniformly to the exact solution. The UWM is applied to three different BBM equations, including a linear, non-homogeneous, and nonlinear case. The results demonstrate that the UWM provides more accurate solutions compared to other methods, especially when the parameter M is increased. The method is efficient and suitable for solving both linear and nonlinear BBM equations. The study concludes that the UWM is a promising approach for solving partial differential equations, particularly the BBM equation.