Abstract
A generalized dimensional analysis performed by using Buckingham's Pi-theorem for the generalized Burgers' equation is presented. The application of the Buckingham Pi-theorem is used to reduce the governing partial differential equation with the boundary and initial conditions to an ordinary differential equation with appropriate corresponding conditions. By using a scaling invariant we simplify the similarity solutions, which are discussed for a specific choice of boundary conditions, and yield analytical solutions, which are in closed form. Also, using extended one-step methods of order five we solve the final ordinary differential equations. This criterion for solvability involves converting the boundary value problem to an initial value problem.