A novel variable-grid finite-difference method for fiber lasers

A novel finite-difference method with a variable discrete grid is proposed. The algorithm is applied to the traveling wave model for fiber lasers successfully. The simulation for the CW and the actively Q-switched output of Yb-doped fiber laser is compared with the reported results and the results simulated by a traditional constant-grid finite difference method. The comparisons prove that the new algorithm causes negligible adverse impacts, while the efficiency is largely improved. The novel algorithm presented in this paper can be optimized to be a promising method for solving other sorts of partial differential equations.