TY - JOUR

T1 - Runge-Kutta stability on a Floquet problem

T2 - DHS test, take out this subtitle when done

AU - Higham, D.J.

PY - 1994/3

Y1 - 1994/3

N2 - 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

AB - 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

KW - Runge-Kutta

KW - absolute stability

KW - Floquet

KW - equilibrium

KW - steady state

KW - numerical mathematics

UR - http://www.lib.strath.ac.uk

UR - http://suprimo.lib.strath.ac.uk/primo_library/libweb/action/search.do?dscnt=1&fromLogin=true&dstmp=1310571492986&vid=SUVU01&fromLogin=true

M3 - Article

SN - 0006-3835

VL - 34

SP - 88

EP - 98

JO - BIT Numerical Mathematics

JF - BIT Numerical Mathematics

IS - 1

ER -