On Fri, 2008-10-03 at 10:50 -0500, Roy Stogner wrote: > On Thu, 2 Oct 2008, Nasser Mohieddin Abukhdeir wrote: > > > Moving back to John's point about the previously mentioned > > Predictor/Corrector algorithm (assuming we compute everything > > correctly), I'm assuming that idea is trashed. > > The idea that we can use the first Newton step as an explicit solution > is wrong, but using a forward Euler solve for the predictor and > following it up by a backward Euler Newton solve for the corrector > should still work just fine.
Are you sure about that? It seems that if delta t is significantly larger than the forward Euler stability criterion, this would make an awful predictor. In the past I've used a linear projection of the previous two timesteps into the new time as the predictor, and saved a couple of Newton iterations vs. using the previous timestep alone, which is more stable than a forward Euler step, but doesn't always work well either... > > I did some digging > > around, looked up the methods that John suggested, and found a variable > > coefficient multistep method (allows for unequally spaced data): > > > > Chapter 12 > > http://books.google.com/books?id=aqfMgehyGnEC > > That looks like an excellent adaptive method for us to use in the > future. I'd still suggest doing a single-step predictor/corrector > first before biting off something more complicated. Good point! Thank you Nasser for taking the initiative in this. -Adam -- GPG fingerprint: D54D 1AEE B11C CE9B A02B C5DD 526F 01E8 564E E4B6 Engineering consulting with open source tools http://www.opennovation.com/
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