Stability of uniformly Morse-Smale gradient-like numerical methods for flows |
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Authors: | Chen Mayru; Li Ming-Chia |
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Institution: |
1 Department of Mathematics, National Changhua University of Education, Changhua 500, Taiwan
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Abstract: | In Garay (1996, Numer. Math., 72, 449479) and Li (1997b,SIAM J. Math. Anal., 28, 381388), it was shown that thequalitative properties of a MorseSmale gradient-likeflow are preserved by its numerical approximations. In thispaper, we show that the qualitative properties of a family ofuniformly MorseSmale gradient-like numerical methodsare preserved by the approximated flow. The techniques usedin the study of the structural stability theorem for diffeomorphismsare the main tools for this work. |
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Keywords: | uniformly Morse Smale gradient-like structural stability numerical method |
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