Stability of uniformly Morse-Smale gradient-like numerical methods for flows
M. Chen · IMA Journal of Numerical Analysis · 2004
In Garay (1996, Numer. Math., 72, 449–479) and Li (1997b, SIAM J. Math. Anal., 28, 381–388), it was shown that the qualitative properties of a Morse–Smale gradient‐like flow are preserved by its numerical approximations. In this paper, we show that the qualitative properties of a family of uniformly Morse–Smale gradient‐like numerical methods are preserved by the approximated flow. The techniques used in the study of the structural stability theorem for diffeomorphisms are the main tools for this work.