Adaptive higher-order split-step Fourier algorithm for simulating lightwave propagation in optical fiber

In this paper, we propose an adaptive step-size control algorithm for solving nonlinear Schrödinger’s equations. The proposed algorithm has a fourth-order local accuracy and is a system-independent rule for adjusting the step sizes. This algorithm has two potential advantages, an automatic step adjustment mechanism and higher-order accuracy. A test example shows that, by comparing to the fixed step-size method and the local-error method, our method decreases the computational time by about 10 and 70 times, respectively. The performance of the proposed method is validated and compared to commonly used step-size selection methods by simulating the evolution of a third-order soliton, the collision of a fundamental soliton pair, and the supercontinuum generation. Numerical simulations show that the proposed method can increase the computational efficiency by more than one and two orders of magnitude in comparison with the symmetrized split-step Fourier method. In addition, the computational efficiency is improved with the increase of the accuracy of solutions.