Abstract
In this paper we study dynamic iteration techniques for systems of nonlinear delay differential equations. After pointing out a close connection to the ‘truncated infinite embedding’, as proposed by Feldstein, Iserles, and Levin, we give a proof of the superlinear convergence of the simple dynamic iteration scheme. Then we propose a more general scheme that in addition allows for a decoupling of the equations into disjoint subsystems, just like what we are used to from dynamic iteration schemes for ODEs. This scheme is also shown to converge superlinearly.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
A. Feldstein, A. Iserles, and D. Levin,Embedding of delay equations into an infinite-dimensional ODE system, to appear in J. Differential Equations.
A. Lelarasmee, A. E. Ruehli, and A. L. Sangiovanni-Vincentelli,The waveform relaxation method for time-domain analysis of large scale integrated circuits, IEEE Trans. on CAD of IC and Syst., 1 (1982), pp. 131–145.
U. Miekkala and O. Nevanlinna,Convergence of dynamic iteration methods for initial value problems, SIAM J. Sci. Stat. Comput., 8 (1987), pp. 459–482.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Bjørhus, M. On dynamic iteration for delay differential equations. BIT 34, 325–336 (1994). https://doi.org/10.1007/BF01935642
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01935642