Finite element collocation approximation of the characteristic exponent in BVPs with periodic coefficients (Q1919494)

In order to determine the characteristic exponents in Floquet's theory for the solution of general second-order homogeneous differential equations with periodic coefficients, the authors propose a finite element collocation method that uses Hermite cubic elements. By applying the fact that the characteristic exponents appear in pairs with opposite sign, they obtain that the equations which determine universal collocation points have as their solution pairs of Gaussian points on each interval. This optimality condition is tested with three examples that put in evidence the superior approach of the authors' method, when compared with the matrix method.