We present a fast and efficient numerical model for Yb3+-doped fiber lasers based on shooting method. The algorithm is based on the assumption of a starting value for the slope efficiency and the evaluation of the pump power threshold. The starting value of slope efficiency is related to initial conditions through the boundary conditions, and it is subsequently optimized by iteration. The method ensures a fast and efficient convergence of the solution of the coupled first-order differential equations that describes the evolution of pump and signal powers in a Yb3+-doped fiber laser. The results of the numerical solution are compared with experimental and published data giving a good agreement
