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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