Stiffness of ODEs

D.J. Higham, L.N. Trefethen

Research output: Contribution to journalArticle

56 Citations (Scopus)

Abstract

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
Volume33
Issue number2
DOIs
Publication statusPublished - Jun 1993

Keywords

  • stiffness
  • stability
  • pseudospectra
  • numerical mathematics

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    Higham, D. J., & Trefethen, L. N. (1993). Stiffness of ODEs. BIT Numerical Mathematics, 33(2), 285-303. https://doi.org/10.1007/BF01989751