Collocation schemes for periodic solutions of neutral delay differential equations

Barton, David A.W., Krauskopf, Bernd and Wilson, R. Eddie (2006) Collocation schemes for periodic solutions of neutral delay differential equations. Journal of Difference Equations and Applications, 12 (11), 1087-1101. (doi:10.1080/10236190601045663).

Record type: Article

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 (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.

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