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Finite Dimensional Approximation of the Monodromy Operator of a Periodic Delay Differential Equation with Piecewise Constant Orthonormal Functions

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Document pages: 23 pages

Abstract: Using piecewise constant orthonormal functions, an approximation of themonodromy operator of a Linear Periodic Delay Differential Equation (PDDE)is obtained by approximating the integral equation corresponding to thePDDE as a linear operator over the space of initial conditions. This approximationallows us to consider the state space as finite dimensional resulting ina finite matrix approximation whose spectrum converges to the spectrum ofthe monodromy operator.

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