On Fri, 3 Oct 2008, Roy Stogner wrote:
>> 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.
Oh, wait - in that chapter, it looks like their corrector step isn't
really an implicit solve - they're not relating y^c_{n+1} to an
implicit function of y^c_{n+1}, they're plugging in the predictor
solution y^p_{n+1} instead. That's fine for local asymptotic
accuracy, but IIRC with typical PDEs you end up losing your ability to
take stable large time steps. It might be an interesting optional
feature, but I think for our default behavior we'd want to do a full
nonlinear implicit solve instead.
So when I say "that looks like an excellent adaptive method for us",
you should instead read "with one slight modification, that would look
like an excellent adaptive method for us".
---
Roy
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