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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Supported by a Dundee University Research Initiatives Grant.
Supported by NSF Grant DMS-9116110.
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Higham, D.J., Trefethen, L.N. Stiffness of ODEs. BIT 33, 285–303 (1993). https://doi.org/10.1007/BF01989751
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DOI: https://doi.org/10.1007/BF01989751