This thesis examines the numerical solution to Burgers' equation on a finite spatial domain with various boundary conditions. We first conduct experiments to confirm the numerical solutions observed by other researchers for Neumann boundary conditions. Then we consider the case where the non-homogeneous Robin boundary conditions approach non-homogeneous Neumann conditions. Finally we numerically approximate the steady state solutions to Burgers' equation with both the homogeneous and non-homogeneous Robin boundary conditions. / Master of Science