Finite element collocation approximation of the characteristic exponent in BVPs with periodic coefficients

We consider the application of the finite element collocation method, with Hermite cubic elements, for the determination of the characteristic exponent in Floquetʹs theory for the solution of the general second order homogeneous differential equation with periodic coefficients. The freedom in choosing the collocation points and the high order of approximation were the main reasons for the employment of the collocation method. The determination of the Gaussian points as optimal interior collocation points gave us the additional advantage of an optimum method. The computational comparison with the classical matrix method reveals the superiority of the collocation method.