Stiffness of ODEs

D.J. Higham, L.N. Trefethen

Research output: Contribution to journalArticlepeer-review

72 Citations (Scopus)


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.
Original languageEnglish
Pages (from-to)285-303
Number of pages18
JournalBIT Numerical Mathematics
Issue number2
Publication statusPublished - Jun 1993


  • stiffness
  • stability
  • pseudospectra
  • numerical mathematics


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