BIT Numerical Mathematics

, Volume 34, Issue 3, pp 325–336 | Cite as

On dynamic iteration for delay differential equations

  • M. Bjørhus


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.

AMS subject classifications

65L05 34K99 

Key words

Delay differential equations dynamic iteration waveform relaxation 


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  1. 1.
    A. Feldstein, A. Iserles, and D. Levin,Embedding of delay equations into an infinite-dimensional ODE system, to appear in J. Differential Equations.Google Scholar
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    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.Google Scholar
  3. 3.
    U. Miekkala and O. Nevanlinna,Convergence of dynamic iteration methods for initial value problems, SIAM J. Sci. Stat. Comput., 8 (1987), pp. 459–482.CrossRefGoogle Scholar

Copyright information

© BIT Foundation 1994

Authors and Affiliations

  • M. Bjørhus
    • 1
  1. 1.Department of Mathematical SciencesThe Norwegian Institute of TechnologyTrondheimNorway

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