A novel fast numerical algorithm for cascaded Raman fiber laser using the analytic approximate solution

In this paper, we proposed a novel numerical algorithm for cascaded Raman fiber laser (CRFL) using the approximate analytic results as the initial values for shooting method, which effectively reduces the calculating time from several hours to a few minutes. With the algorithm, we obtained a numerical solution of the bilateral-pumping Ge-doped fifth-order CRFL which can avoid the so-called “end face damage” phenomenon efficiently. At the same time, we also simulated the unilateral-pumping one as a comparison, which showed both the characteristics of them are similar with each other.     

Solving boundary value problems of ordinary differential equations with non-separated boundary conditions

This paper focuses on solving the two point boundary value problem, in which boundary conditions are systems of nonlinear equations. The shooting method was used together with a combination of Newton’s method and Broyden’s method, to update the initial values of the differential equations. The experiments showed that the proposed method performed well, in the sense that the overall amount of work was less than that of the Newton Shooting method.