Fig. 1. Schematic diagram of all-normal-dispersion passively mode-locked Er-doped fiber laser

Fig. 2. The relationship between global error and the local energy increment δ

Fig. 3. Energy evolution within a local step in each loop

Fig. 4. The spectra of dissipative soliton. (a) SSFM-GELE method; (b) SSFM-fine method

Fig. 5. The temporal intensity of dissipative soliton

Fig. 6. Results from numerical simulation of dissipative soliton showing temporal evolution of the pulse in cavity. (a) By the SSMF-GELE method. (b) By the SSMF-Fine method. Both (a) and (b) are color map. (c) and (d) are waveforms over the propagation loop of 300.

Fig. 7. Global error and the computational time calculated by GELE and constant methods