Runge-Kutta stability on a Floquet problem

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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
Original languageEnglish
Pages (from-to)88-98
Number of pages11
JournalBit numerical mathematics
Issue number1
Publication statusPublished - Mar 1994


  • Runge-Kutta
  • absolute stability
  • Floquet
  • equilibrium
  • steady state
  • numerical mathematics

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