Excellent initial guess functions for simple shooting method in Yb3+-doped fiber lasers

•The paper provides two excellent initial guess functions for simple shooting method.•The excellent initial guess functions overcome the difficulty of setting initial values.•The simulation results using simple shooting method agree with those by NSTM-BVPs.•The critical guess value of slope efficiency is less than 0.3 in initial guess functions.

Excellent initial guess functions, providing for setting suitable initial estimates for simple shooting method, are developed to solve high power Yb3+-doped fiber lasers model with boundary conditions. When the guess value of slope efficiency is greater than or equal to the critical guess value of slope efficiency, the initial guess values of the forward signal power and backward pump power, generating from the excellent initial guess functions, are good initial guess values for the simple shooting method. Then, comparing the simulation results using our simple shooting method and the number sequence transition method based on MATLAB BVP solvers (NSTM-BVPs), the difference of the simulation results are less than given absolute error tolerance for different fiber length. Finally, we can conclude that the critical guess value of slope efficiency is less than 0.3 for all the fiber length, Yb3+-doped concentration, signal reflectivity and pump power.