Runge-Kutta stability on a Floquet problem |
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Authors: | Higham Desmond J. |
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Affiliation: | (1) Department of Mathematics and Computer Science, University of Dundee, DD1 4HN Dundee |
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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.Supported by the University of Dundee Research Initiatives Fund. |
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Keywords: | Runge-Kutta absolute stability Floquet equilibrium steady state |
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