SSFM-global-error-local-energy method for improving computational efficiency of passively mode-locked fiber laser

We propose a method for improving the computational efficiency of passively mode-locked fiber laser, which is composed by Symmetric Split-step Fourier Method (SSFM) and the Global-Error-Local -En-ergy (GELE) method for solving propagating equations. Our proposed method relies on the limitation of loc-al energy increment related with global error within a certain value to control the selection of step size. This method has advantage of an automatic step adjustment mechanism. To achieve the same order of computa-tion accuracy, the computational time of our method is 255 s, while SSFM with small constant step size method needs to calculate 3 855 s. The computational time of our proposed method is one or two orders of magnitude less than that of the SSFM, which indicates our method can enhance the computational efficiency by a factor up to 10. It could be expanded with high-order algorithms, such as the fourth-order Runge-Kutta in the interaction picture (RK4IP), Adams, predictor-corrector, etc. for improving the accuracy.