We present a Galerkin projection technique by which finite-dimensional ODE approximations for DDE’s can be obtained in a straightforward fashion. The technique requires neither the system to be near a bifurcation point, nor the delayed terms to have any specific restrictive form, nor even the delay, nonlinearities and/or forcing to be small. We show through several numerical examples that the systems of ODE’s obtained using this procedure can accurately capture the dynamics of the DDE’s under study, and that the accuracy of solutions increases with increasing numbers of shape functions used in the Galerkin projection. Examples studied here include a linear constant coefficient DDE as well as forced nonlinear DDE’s with one or more delays and possibly nonlinear delayed terms. Parameter studies, with associated bifurcation diagrams, show that the qualitative dynamics of the DDE’s can be captured satisfactorily with a modest number of shape functions in the Galerkin projection.
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ASME 2003 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
September 2–6, 2003
Chicago, Illinois, USA
Conference Sponsors:
- Design Engineering Division and Computers and Information in Engineering Division
ISBN:
0-7918-3703-3
PROCEEDINGS PAPER
Galerkin Projections for Delay Differential Equations
Pankaj Wahi,
Pankaj Wahi
Indian Institute of Science, Bangalore, India
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Anindya Chatterjee
Anindya Chatterjee
Indian Institute of Science, Bangalore, India
Search for other works by this author on:
Pankaj Wahi
Indian Institute of Science, Bangalore, India
Anindya Chatterjee
Indian Institute of Science, Bangalore, India
Paper No:
DETC2003/VIB-48570, pp. 2211-2220; 10 pages
Published Online:
June 23, 2008
Citation
Wahi, P, & Chatterjee, A. "Galerkin Projections for Delay Differential Equations." Proceedings of the ASME 2003 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. Volume 5: 19th Biennial Conference on Mechanical Vibration and Noise, Parts A, B, and C. Chicago, Illinois, USA. September 2–6, 2003. pp. 2211-2220. ASME. https://doi.org/10.1115/DETC2003/VIB-48570
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