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Science Forum Index » Math - Numerical Analysis Forum » Solution converges and then diverges
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Message |
| Guest |
 Posted: Thu Mar 15, 2007 4:15 pm |
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I am solving a partial differential equation by explicitly
discretizing it. I am using very small time step to prevent
instability. However, one thing I noticed is that the software reaches
a very good solution after some number of iterations but then it
starts to diverge. Therefore the result changes as the number
iterations change. I was hoping to reach a steady state solution, but
I don't. Why would be the reason? Can anyone please show a few
pointers? Thanks |
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| Peter Spellucci |
| Posted: Fri Mar 16, 2007 6:20 am |
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Guest
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In article <1173993336.022278.211920@y66g2000hsf.googlegroups.com>,
po2121@dodgeit.com writes:
Quote: I am solving a partial differential equation by explicitly
discretizing it. I am using very small time step to prevent
instability. However, one thing I noticed is that the software reaches
a very good solution after some number of iterations but then it
starts to diverge. Therefore the result changes as the number
iterations change. I was hoping to reach a steady state solution, but
I don't. Why would be the reason? Can anyone please show a few
pointers? Thanks
since you speak about an explicit discretization, I assume by "iteration"
you mean a time step. well, the form of the error bound for such methods
is something like
norm(u(.,t)-u^h(.,t)) <= C(t)*(timestep^p+spacestep^q)
+ (t/timestep)*C_1*machine_epsilon
hence there is a slow blow up due to roundoff, but if you integrate
over a long time interval with very small timesteps there will be finally a
blow up. this is not the case if you use an dissipative scheme which damps away
errors back in time
hth
peter |
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