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Numerische Mathematik

, Volume 56, Issue 5, pp 469–499 | Cite as

Asymptotic error expansions for stiff equations: an analysis for the implicit midpoint and trapezoidal rules in the strongly stiff case

  • W. Auzinger
  • R. Frank
Article

Summary

The structure of the global discretization error is studied for the implicit midpoint and trapezoidal rules applied to nonlinearstiff initial value problems. The point is that, in general, the global error contains nonsmooth (oscillating) terms at the dominanth2-level. However, it is shown in the present paper that for special classes of stiff problems these nonsmooth terms contain an additional factor ɛ (where-1/ɛ is the magnitude of the stiff eigenvalues). In these cases a “full” asymptotic error expansion exists in thestrongly stiff case (ε sufficiently small compared to the stepsizeh). The general case (where the oscillating error components areO(h2) and notO(ɛh2)) and applications of our results (extrapolation and defect correction algorithims) will be studied in separate papers.

Subject Classifications

AMS(MOS): 65L05 65L07 CR: G1.7 

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References

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Copyright information

© Springer-Verlag 1989

Authors and Affiliations

  • W. Auzinger
    • 1
  • R. Frank
    • 1
  1. 1.Institut für Angewandte und Numerische MathematikTechnische Universität WienAustria

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