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Abstract

If an ordinary differential equation is solved by using a linear multistep method, then it is well-known that the asymptotic behaviour of the error is determined by the characteristic roots of the discretized differential equation. In particular the so-called essential roots (the roots on or close to the unit circle) play an important rôle. If a functional differential equation is solved by means of a linear multistep method, then the number of characteristic roots of the discretized equation is inversely proportional to the stepsize used. In this paper it is shown that only a fixed number of these roots are strictly inside the unit circle, and all the others are “essential”.

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References

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    Bellman, R.E., and K.L. Cooke, Differential-difference equations, Academic Press, 1966.Google Scholar
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Copyright information

© Springer Basel AG 1983

Authors and Affiliations

  • Maarten de Gee
    • 1
  1. 1.Mathematisch InstituutRijksuniversiteit UtrechtUtrechtThe Netherlands

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