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Collocation schemes for periodic solutions of neutral delay differential equations. (English) Zbl 1108.65089
Summary: We introduce two collocation schemes for the computation of periodic solutions of neutral delay differential equations (NDDEs): one based on a direct discretisation of the underlying NDDE, and one based on a discretisation of a related delay differential difference equation (i.e. a delay differential equation (DDE) coupled with a difference equation). Numerical examples are used to demonstrate these schemes and their respective orders of convergence. Both collocation schemes are implemented in DDE-BIFTOOL, a numerical continuation tool for delay equations. Their use in a continuation setting is shown with one- and two-parameter bifurcation studies of a transmission line model.

MSC:
65L60 Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations
34K28 Numerical approximation of solutions of functional-differential equations (MSC2010)
34K18 Bifurcation theory of functional-differential equations
34K13 Periodic solutions to functional-differential equations
Software:
DDE-BIFTOOL; RADAR5
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