G-stability is equivalent toA-stability
Copyright policy )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.
numerical solution, multistep methods, ordinary differential equations, accumulated error estimates, non-linear stiff problems, Numerical investigation of stability of solutions to ordinary differential equations, A-stability, Numerical methods for initial value problems involving ordinary differential equations, G-stability
numerical solution, multistep methods, ordinary differential equations, accumulated error estimates, non-linear stiff problems, Numerical investigation of stability of solutions to ordinary differential equations, A-stability, Numerical methods for initial value problems involving ordinary differential equations, G-stability
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