On Fri, Oct 3, 2008 at 12:40 PM, Adam C Powell IV <[EMAIL PROTECTED]> wrote:
> 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 (assumi
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 exce
On Thu, 2 Oct 2008, John Peterson wrote:
> This was probably a confusing description but try it for
> a simple example to convince yourself the first Newton step is not the
> same as an explicit solve.
John's right - in fact, consider the case where f(U) is linear. Then
Newton will obviously h
On Thu, Oct 2, 2008 at 1:41 PM, Nasser Mohieddin Abukhdeir
<[EMAIL PROTECTED]> wrote:
> Hello all:
>After some enlightening conversations with Roy, I am going to be
> implementing a predictor/corrector AdaptiveTimeSolver class that does
> the following:
>
> 1) An explicit solve (just an EulerSo
On Fri, 2008-10-03 at 12:58 -0500, John Peterson wrote:
> On Fri, Oct 3, 2008 at 12:40 PM, Adam C Powell IV <[EMAIL PROTECTED]> wrote:
> > 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 t
On Fri, 3 Oct 2008, Adam C Powell IV wrote:
> 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
>>> corr
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.
>
> T
On Thu, 2 Oct 2008, Nasser Mohieddin Abukhdeir wrote:
> What now confuses me is whether or not EulerSolver with theta=0.5 is
> actually Crank-Nicolson. It makes sense to me that Euler2Solver with
> theta=0.5 is...but not EulerSolver.
That actually depends on your definition of Crank-Nicholson.
You may want to look at this excellent book on continuation methods. It
includes pseudo-code for several robust Newton-type predictor-corrector
methods, including bifurcation detection. Most of the book is not
specifically transient, but it should be helpful anyway.
@book{allgower2003inc,
titl
ok, John's explanation was very helpful, did the math (a few times :)
and have a better grasp on the problem then I did before, sorry about that.
What now confuses me is whether or not EulerSolver with theta=0.5 is
actually Crank-Nicolson. It makes sense to me that Euler2Solver with
theta=0.5 i
On Thu, Oct 2, 2008 at 3:12 PM, Nasser Mohieddin Abukhdeir
<[EMAIL PROTECTED]> wrote:
> Just to clarify things, my understanding of the backwards Euler method that
> is implemented now is such that for the initial u' = f(theta*u_new +
> (1-theta)*u_old), so the first iteration of the nonlinear solv
Just to clarify things, my understanding of the backwards Euler method
that is implemented now is such that for the initial u' = f(theta*u_new
+ (1-theta)*u_old), so the first iteration of the nonlinear solver
should be equivalent to an explicit solve, assuming u_new = u_old during
the first st
Hello all:
After some enlightening conversations with Roy, I am going to be
implementing a predictor/corrector AdaptiveTimeSolver class that does
the following:
1) An explicit solve (just an EulerSolver step with theta=0) yields the
"predictor" which is stored.
2) The explicit solve soluti
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