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 | | From: | Fan Yang | | Subject: | Bound of the difference between ODE and discretized system? | | Date: | Sat, 20 Nov 2004 00:14:53 -0600 |
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 | Dear all,
First we have an ODE system
dx/dt = f(x), x belongs to R^n. There exists a unique
globally asymptotically stable fixed point.
If we do a smooth approximation by a discretized system,
x(t+1) = (1-b(t))*x(t) + b(t)*f(x(t)), where b(t) is small.
Then within a finite time, can we give an upper bound of
the distance between ODE and the discretized system above?
I was told that this distance should go to zero if the b(t) is
very small everywhere. Can somebody give me a reference
of this statement? Btw, if we take the form b(t) = 1/t, can
we get an upper bound of the difference?
Thanks a lot for your help,
Fan
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