Spijker’s Example and Its Extension

  • Miklós E. MincsovicsEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11386)


Strongly and weakly stable linear multistep methods can behave very differently. The latter class can produce spurious oscillations in some of the cases for which the former class works flawlessly. The main question is if we can find a well defined property which clearly tells the difference between them. There are many explanations from different viewpoints. We cite Spijker’s example which shows that the explicit two step midpoint method is unstable with respect to the Spijker norm. We show that this result can be extended for the general weakly stable case.


Linear multistep methods Stability Spijker-norm 


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Authors and Affiliations

  1. 1.MTA-ELTE Numerical Analysis and Large Networks Research GroupBudapestHungary
  2. 2.Department of Differential EquationsBudapest University of Technology and EconomicsBudapestHungary

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