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

D.J. Higham

Research output: Contribution to journalArticle

1 Citation (Scopus)

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
Original languageEnglish
Pages (from-to)88-98
Number of pages11
JournalBIT Numerical Mathematics
Volume34
Issue number1
Publication statusPublished - Mar 1994

Keywords

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

Fingerprint Dive into the research topics of 'Runge-Kutta stability on a Floquet problem: DHS test, take out this subtitle when done'. Together they form a unique fingerprint.

  • Cite this