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Collocation schemes for periodic solutions of neutral delay differential equations

Collocation schemes for periodic solutions of neutral delay differential equations
Collocation schemes for periodic solutions of neutral delay differential equations
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.
ndde, continuation, bifurcation analysis, collocation polynomial
1023-6198
1087-1101
Barton, David A.W.
3003bb1f-d648-4d00-a309-8ab75f333df0
Krauskopf, Bernd
a4fa8a40-8801-45d6-bb33-97f25ee166f1
Wilson, R. Eddie
01d7f1f2-f8ee-4661-b713-dcefcddb89bd
Barton, David A.W.
3003bb1f-d648-4d00-a309-8ab75f333df0
Krauskopf, Bernd
a4fa8a40-8801-45d6-bb33-97f25ee166f1
Wilson, R. Eddie
01d7f1f2-f8ee-4661-b713-dcefcddb89bd

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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More information

Published date: 2006
Keywords: ndde, continuation, bifurcation analysis, collocation polynomial

Identifiers

Local EPrints ID: 184257
URI: http://eprints.soton.ac.uk/id/eprint/184257
ISSN: 1023-6198
PURE UUID: 4b94a28a-845c-4767-aece-e72d862d9155

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Date deposited: 12 May 2011 08:51
Last modified: 16 Jul 2019 23:40

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