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Runge-Kutta stability on a Floquet problem : DHS test, take out this subtitle when done

Higham, D.J. (1994) Runge-Kutta stability on a Floquet problem : DHS test, take out this subtitle when done. BIT Numerical Mathematics, 34 (1). pp. 88-98. ISSN 0006-3835

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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. DOI: 10.1007/BF01935018