TITLE:
Finite Dimensional Approximation of the Monodromy Operator of a Periodic Delay Differential Equation with Piecewise Constant Orthonormal Functions
AUTHORS:
Eli A. Vazquez, Joaquin Collado
KEYWORDS:
Monodromy Operator, Periodic Delay Differential Equations, Walsh Functions, Block Pulse Functions, Finite Rank Approximation
JOURNAL NAME:
Applied Mathematics,
Vol.9 No.11,
November
30,
2018
ABSTRACT: Using piecewise constant orthonormal functions, an approximation of the
monodromy operator of a Linear Periodic Delay Differential Equation (PDDE)
is obtained by approximating the integral equation corresponding to the
PDDE as a linear operator over the space of initial conditions. This approximation
allows us to consider the state space as finite dimensional resulting in
a finite matrix approximation whose spectrum converges to the spectrum of
the monodromy operator.