Collocation schemes for periodic solutions of neutral delay differential equations

DAW Barton, B Krauskopf, RE Wilson

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Abstract

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 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.
Original languageEnglish
Publication statusPublished - 2005

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