  We propose an implementation of a method based on Fourier analysis to obtain
the Floquet characteristic exponents for periodic homogeneous linear systems,
which shows a high precision. This implementation uses a variational principle
to find the correct Floquet exponents among the solutions of an algebraic
equation. Once we have these Floquet exponents, we determine explicit
approximated solutions. We test our results on systems for which exact
solutions are known to verify the accuracy of our method. Using the equivalent
linear system, we also study approximate solutions for homogeneous linear
equations with periodic coefficients.
