Stiffness of ODEs

D.J. Higham; L.N. Trefethen

doi:10.1007/BF01989751

Stiffness of ODEs

D.J. Higham, L.N. Trefethen

Mathematics And Statistics

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82 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 language	English
Pages (from-to)	285-303
Number of pages	18
Journal	BIT Numerical Mathematics
Volume	33
Issue number	2
DOIs	https://doi.org/10.1007/BF01989751
Publication status	Published - Jun 1993

Keywords

stiffness
stability
pseudospectra
numerical mathematics

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10.1007/BF01989751

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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.",

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AU - Higham, D.J.

AU - Trefethen, L.N.

PY - 1993/6

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N2 - 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.

AB - 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.

KW - stiffness

KW - stability

KW - pseudospectra

KW - numerical mathematics

UR - http://dx.doi.org/10.1007/BF01989751

U2 - 10.1007/BF01989751

DO - 10.1007/BF01989751

M3 - Article

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VL - 33

SP - 285

EP - 303

JO - BIT Numerical Mathematics

JF - BIT Numerical Mathematics

IS - 2

ER -

Stiffness of ODEs

Abstract

Keywords

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