Finite Dimensional Approximation of the Monodromy Operator of a Periodic Delay Differential Equation with Piecewise Constant Orthonormal Functions ()
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.
Share and Cite:
Vazquez, E. and Collado, J. (2018) Finite Dimensional Approximation of the Monodromy Operator of a Periodic Delay Differential Equation with Piecewise Constant Orthonormal Functions.
Applied Mathematics,
9, 1315-1337. doi:
10.4236/am.2018.911086.