Stiffness of ODEs

D.J. Higham, L.N. Trefethen

Research output: Contribution to journalArticle

53 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.
LanguageEnglish
Pages285-303
Number of pages18
JournalBIT Numerical Mathematics
Volume33
Issue number2
DOIs
Publication statusPublished - Jun 1993

Fingerprint

Stiffness
Pseudospectra
Eigenvalue
Linear systems
Linear Systems
Numerical Experiment
Numerical Solution
Coefficient
Experiments

Keywords

  • stiffness
  • stability
  • pseudospectra
  • numerical mathematics

Cite this

Higham, D. J., & Trefethen, L. N. (1993). Stiffness of ODEs. BIT Numerical Mathematics, 33(2), 285-303. https://doi.org/10.1007/BF01989751
Higham, D.J. ; Trefethen, L.N. / Stiffness of ODEs. In: BIT Numerical Mathematics. 1993 ; Vol. 33, No. 2. pp. 285-303.
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Higham, DJ & Trefethen, LN 1993, 'Stiffness of ODEs' BIT Numerical Mathematics, vol. 33, no. 2, pp. 285-303. https://doi.org/10.1007/BF01989751

Stiffness of ODEs. / Higham, D.J.; Trefethen, L.N.

In: BIT Numerical Mathematics, Vol. 33, No. 2, 06.1993, p. 285-303.

Research output: Contribution to journalArticle

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Higham DJ, Trefethen LN. Stiffness of ODEs. BIT Numerical Mathematics. 1993 Jun;33(2):285-303. https://doi.org/10.1007/BF01989751