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IMA Journal of Numerical Analysis 2004 24(4):577-585; doi:10.1093/imanum/24.4.577
© 2004 by Institute of Mathematics and its Applications
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Stability of uniformly Morse–Smale gradient-like numerical methods for flows

Mayru Chen1 and Ming-Chia Li1

1 Department of Mathematics, National Changhua University of Education, Changhua 500, Taiwan

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.

Key Words: uniformly Morse–Smale; gradient-like; structural stability; numerical method

Received 7 November 2003. Revised 19 February 2004.


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