Abstract
Over recent decades, fiber Raman lasers (FRLs) have received much attention
from researchers and have become a challenge for them both numerically and
experimentally. The equations governing the FRLs are in the form of a first-order
system of nonlinear two-point boundary-value ordinary differential equations.
In this paper, an algorithm for solving this system of differential equations
using a spectral method, namely Chebyshev pseudospectral method, is presented
in detail and then numerical simulations are performed. The main advantage
of the spectral methods is in their optimality in achieving high accuracy
by using fewer degrees of freedom under suitable conditions. It is shown that
the proposed spectral method in combination with the Newton method results
in a considerable reduction in the size of the discretized problem and in
the computational effort to achieve high accuracy. In this paper, a new approach
for constructing an initial approximate solution for the Newton iteration
is also presented.
© 2009 IEEE
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