Number sequence transition method based on MATLAB BVP solvers for high power Yb3+-doped fiber lasers

• Number sequence transition method can update automatically the initial trial values.
• Comparing other methods, NSTM-BVPs overcome the difficulty of setting initial values.
• NSTM-BVPs can be set randomly initial value without foreknowledge.
• Average iteration times of NSTM-BVPs are less than 2 for desired high accuracy.
• NSTM-BVPs are valid for different laser output mirror reflectivity and SBS threshold.

A number sequence transition method based on MATLAB BVP solvers (NSTM-BVPs) for high power Yb3+-doped fiber lasers with boundary conditions is proposed. The results demonstrate that the NSTM-BVPs can automatically update the initial trial values to deal with the difficulty of setting unreasonable initial values in MATLAB BVP solvers. The number sequence transition method based on bvp6c (NSTM-bvp6c) is then discovered to be superior to NSTM-bvp4c and NSTM-bvp5c. Further, when we set the arbitrary initial value without foreknowledge, the efficiency of NSTM-BVPs is also verified with different pump structures, pump powers, pump reflections and laser output mirror reflectivity. Finally, compared with the shooting method, relaxation method and related experiment, the NSTM-BVPs is valid, and the stimulated Brillouin scattering (SBS) threshold is obtained successfully by NSTM-BVPs.