Summary.
In this paper the (long time) stability of numerical methods for a class of nonlinear autonomous differential systems possessing a semi-stable equilibrium, is considered. The local dynamics of the class under the H-assumptions is reviewed. Some interesting differential systems of stiff type are seen to belong to this class. It is also shown that the Implicit Euler method is the only one of practical interest which is unconditionally stable.
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Mathematics Subject Classification (2000): 65L20, 47H10, 37G05
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González-Pinto, S. Differential systems with semi-stable equilibria and numerical methods. Numer. Math. 96, 253–268 (2003). https://doi.org/10.1007/s00211-003-0461-1
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DOI: https://doi.org/10.1007/s00211-003-0461-1