BIT Numerical Mathematics

, Volume 33, Issue 2, pp 285–303 | Cite as

Stiffness of ODEs

  • Desmond J. Higham
  • Lloyd N. Trefethen
Part II Numerical Mathematics


It is argued that even for a linear system of ODEs with constant coefficients, stiffness cannot properly be characterized in terms of the eigenvalues of the Jacobian, because stiffness is a transient phenomenon whereas the significance of eigenvalues is asymptotic. Recent theory from the numerical solution of PDEs is adapted to show that a more appropriate characterization can be based upon pseudospectra instead of spectra. Numerical experiments with an adaptive ODE solver illustrate these findings.

AMS(MOS) Subject classification


Key words

stiffness stability pseudospectra 


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Copyright information

© BIT Foundation 1993

Authors and Affiliations

  • Desmond J. Higham
    • 1
    • 2
  • Lloyd N. Trefethen
    • 1
    • 2
  1. 1.Department of Mathematics and Computer ScienceUniversity of DundeeDundeeScotland
  2. 2.Department of Computer ScienceCornell UniversityIthacaUSA

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