论文信息 - G-stability is equivalent toA-stability

G-stability is equivalent toA-stability

In 1975 the author showed that a norm (Liapunov function) can be constructed for the stability and error analysis of a linear multistep method (and the related one-leg method) for the solution of stiff non-linear systems, provided that the system satisfies a monotonicity condition and the method possesses a property calledG-stability.In this paper it is shown thatG-stability is equivalent toA-stability. More generally, a Liapunov function exists if the stability region of the method contains a circle (half-plane), provided that the system satisfies a monotonicity condition related to this circle (half-plane). In the general case this condition depends on the stepsize.

Germund Dahlquist | G. Dahlquist

[1] O. Nevanlinna. On error bounds forG-stable methods , 1976 .

[2] K. Burrage,et al. Stability Criteria for Implicit Runge–Kutta Methods , 1979 .

[3] Germund Dahlquist,et al. Positive Functions and some Applications to Stability Questions for Numerical Methods , 1978 .

[4] Nonlinear fixed-h stability of linear multistep formulas , 1977 .

[5] G. Dahlquist. A special stability problem for linear multistep methods , 1963 .

[6] Olavi Nevanlinna,et al. On the numerical integration of nonlinear initial value problems by linear multistep methods , 1977 .

[7] Werner Liniger,et al. Contractive methods for stiff differential equations part I , 1978 .

[8] H. Kreiss. Difference Methods for Stiff Ordinary Differential Equations , 1978 .

[9] O. Taussky. Matrices C with Cn → 0 , 1964 .