Abstract:The steady-state Burgers equation with high Reynolds number is a singularly perturbed boundary value problem. In order to depress the singularity we consider a coordinate transformation from the z-domain to the t-domain. Then we construct a very effective Lie-group shooting method to search a missing initial condition of slope through a weighting factor r ∈(0,1). Furthermore, a closed-form formula is derived to calculate the unknown slope in terms of r in a more refined range identified. Numerical examples were examined to show that the new approach has high efficiency and high accuracy.