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Numerische Mathematik

, Volume 35, Issue 3, pp 343–354 | Cite as

Vorzeichenstabile Differenzenverfahren für parabolische Anfangsrandwertaufgaben

  • K. Glashoff
  • H. Kreth
Sign-Stability in Difference Schemes for Parabolic Initinal-Boundary Value Problems

Sign-stability in difference schemes for parabolic initial-boundary value problems

Summary

In this paper we consider certain structure conserving properties of finite difference methods for the solution of parabolic initial-boundary value problems. We are interested in conditions on the step size ratio μ=Δtx2 in one-step methods which guarantee that the number of sign changes of the discrete approximation does not increase while proceeding from one time level to the following one. This means that difference schemes of this type possess a so-called variation-diminishing property which is known to hold for continuous diffusion equations also. It turns out that our conditions on μ are stronger than the classical ones which imply the maximum principle for the finite difference equations. By means of an example we show that our sign stability condition is necessary too.

Subject Classification

AMS (MOS) 65N05 

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Copyright information

© Springer-Verlag 1980

Authors and Affiliations

  • K. Glashoff
    • 1
  • H. Kreth
    • 1
  1. 1.Institut für Angewandte MathematikUniversität Hamburg2 Hamburg 13Germany (Fed. Rep.)

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