Finite Difference Simulation of the Viscous Burgers’ Equation with External Source

This study presents a numerical investigation of the viscous Burgers’ equation subjected to an external sinusoidal source term, utilizing an explicit finite difference method. The model incorporates nonlinear advection, viscous diffusion, and spatially varying forcing, representing a physically relevant nonlinear partial differential equation. The numerical scheme uses forward time stepping, upwind discretization for the convective term, and central differencing for the diffusive term. Through simulation, the evolution of the solution profile is visualized using 3D surface plots, space-time contours, and cross-sectional curves. The results demonstrate a consistent amplification near the domain center due to the source term and show the smoothing influence of viscosity over time. The study also addresses the scheme's stability and convergence under suitable discretization parameters. Key Words: Viscous Burgers’ equation, nonlinear PDE, finite difference method, source term, numerical simulation, stability analysis, space-time evolution