<p>Burgers equation, a classic model in fluid dynamics and nonlinear partial differential equations (PDEs), continues to challenge researchers due to its intricate behaviour, especially under high Reynolds numbers (i.e., low viscosity), leading to the convection-dominating effect. In this study, we introduce an improved approach based on collocation-based Legendre pseudospectral method to address multidimensional non-linear viscous Burgers equation. By employing Legendre Gauss-Lobatto points for constructing differentiation matrices, we discretize the equation using proposed technique, leading to a system of ordinary differential equations (ODEs). We then employ the robust fourth-order Runge–Kutta method to solve these ODEs, ensuring stability and accuracy. Numerical experiments are performed to assess the efficacy and robustness of the proposed method. We conducted a thorough comparison with existing models and methods to evaluate the advantages of our approach. The proposed method demonstrates commendable performance, showing significant improvements in accuracy, stability, and computational efficiency.</p>