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  • Floquet  (1)
  • pseudospectra  (1)
  • 1
    Electronic Resource
    Electronic Resource
    Runge-Kutta stability on a Floquet problem (1994)
    Springer
    BIT 34 (1994), S. 88-98 
    Details
    ISSN: 1572-9125
    Keywords: Runge-Kutta ; absolute stability ; Floquet ; equilibrium ; steady state ; 65L05
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract This work examines the stability of explicit Runge-Kutta methods applied to a certain linear ordinary differential equation with periodic coefficients. On this problem naïve use of the eigenvalues of the Jacobian results in misleading conclusions about stable behaviour. It is shown, however, that a valid analogue of the classical absolute stability theory can be developed. Further, using a suitable generalisation of the equilibrium theory of Hall [ACM Trans. on Math. Soft. 11 (1985), pp. 289–301], accurate predictions are made about the performance of modern, adaptive algorithms.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01935018
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Stiffness of ODEs (1993)
    Springer
    BIT 33 (1993), S. 285-303 
    Details
    ISSN: 1572-9125
    Keywords: 65L05 ; stiffness ; stability ; pseudospectra
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: 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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01989751
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    Paper (German National Licenses)
    Fulltext
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