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 -