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Stiffness of ODEs

Higham, D.J. and Trefethen, L.N. (1993) Stiffness of ODEs. BIT Numerical Mathematics, 33 (2). pp. 285-303. ISSN 0006-3835

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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.