This paper introduces a novel numerical method, the ultraspherical wavelet method (UWM), for solving the Benjamin-Bona-Mahony (BBM) equation. The UWM combines the collocation method with ultraspherical wavelets to provide a precise and efficient solution. The method is applied to both linear and nonlinear BBM equations, demonstrating its effectiveness and accuracy. The authors compare the results with other methods, including the finite difference method (FDM) and the Haar wavelet method (HWM), showing that the UWM offers better accuracy. The UWM is characterized by its simplicity, computational efficiency, and flexibility. The convergence analysis of the UWM is presented through a theorem, and the method is validated through numerical experiments and error analysis. The study concludes that the UWM is highly efficient for solving linear and nonlinear BBM equations and can be extended to higher-order equations with minor adjustments.This paper introduces a novel numerical method, the ultraspherical wavelet method (UWM), for solving the Benjamin-Bona-Mahony (BBM) equation. The UWM combines the collocation method with ultraspherical wavelets to provide a precise and efficient solution. The method is applied to both linear and nonlinear BBM equations, demonstrating its effectiveness and accuracy. The authors compare the results with other methods, including the finite difference method (FDM) and the Haar wavelet method (HWM), showing that the UWM offers better accuracy. The UWM is characterized by its simplicity, computational efficiency, and flexibility. The convergence analysis of the UWM is presented through a theorem, and the method is validated through numerical experiments and error analysis. The study concludes that the UWM is highly efficient for solving linear and nonlinear BBM equations and can be extended to higher-order equations with minor adjustments.