Growth conditions on the resolvent of linear operators are useful tools for analysing stability of numerical methods in the solution of linear initial value problems.

Ritt (1953) formulated such a condition under which he proved a form of weak stability. In this talk we show that Ritt's condition can be related to various other resolvent conditions, some of which were considered in the (recent) literature. Furthermore, we prove that Ritt's condition, as well as several akin conditions, actually imply strong stability. Finally, we indicate the relevance of the resolvent conditions under consideration to the analysis of numerical processes.

The work was prepared in collaboration with D. Drissi and M.N. Spijker.

MINISIMPOSIUM SESSION: 16. Stability Issues for IVP methods