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Re: For Loop and NDSolve
*To*: mathgroup at smc.vnet.net
*Subject*: [mg85254] Re: For Loop and NDSolve
*From*: "Jean-Marc Gulliet" <jeanmarc.gulliet at gmail.com>
*Date*: Mon, 4 Feb 2008 03:14:55 -0500 (EST)
*References*: <fnuh4s$9ni$1@smc.vnet.net> <47A4A595.4000601@gmail.com>
PV wrote:
> I am trying to solve a time dependent ordinary differential equation
> of matrices. Here my coefficient matrices in the DE change at every
> instant of time, depending on the solution of the DE in the previous
> instant( feed back type problem). To implement this I use NDSolve with
> a For loop in time. This works fine for certain size of my matrices
> but has got me into trouble for other sizes. I run out of memory
> pretty quickly. I have 1 GB Ram with an AMD X2 duo core 1.7GHZ
> processor.
> Here are the routines that cause problems::
>
> N0 = 1921(large number)
<snip>
Here, I believe you mean something like N0 = 1921(* large number *)
rather than N0 = 1921 \times (large \times number).
Even though, the peace of code is not working independently.
In[1]:= N0 = 1921(* large number *)
For[j = 1, j <= 100, t = j*delt;
solnmatrix =
SparseArray[{{i_,
i_} -> (-V0[a]/2 + ((i - (4*N0 + 1))*k0 - 2*t)^2), {m_, n_} /;
Abs[m - n] == N0 -> -V0[a]/4}, {24*N0 + 1, 24*N0 + 1}];
Print["pbegin ", MemoryInUse[]];
soln = NDSolve[{I*c3*u'[p] == solnmatrix.u[p], u[0] == wavefn},
u, {p, 0, delt}];
Print["p1 ", MemoryInUse[]];
wavefn = First[u[delt] /. soln];
Clear[solnmatrix];
Clear[soln];
Print["p2 ", MemoryInUse[]];
C1 = (Tr[Abs[wavefn]^2/2] +
0.25*Sum[
Conjugate[wavefn[[n]]]*wavefn[[n + N0]], {n, 1, 23*N0 + 1}] +
0.25*Sum[
Conjugate[wavefn[[n]]]*wavefn[[n - N0]], {n, N0 + 1,
24*N0 + 1}])*L;
b = -\[Eta]/(I*\[Gamma]*
C1 - \[Kappa]) + ((\[Eta] + (I*\[Gamma]*C1 - \[Kappa])*
a)/(I*\[Gamma]*C1 - \[Kappa]))*
E^(delt*Tb*(I*\[Gamma]*C1 - \[Kappa]));
a = b;
AppendTo[fieldlist3, a];
AppendTo[normlist, L*Tr[Abs[wavefn]^2]];
AppendTo[couplinglist, C1];
j++;
Print["pend ", MemoryInUse[]];]
Out[1]= 1921
During evaluation of In[1]:= pbegin 20397464
During evaluation of In[1]:= NDSolve::ndnl: Endpoint delt in \
{p,0.,delt} is not a real number. >>
During evaluation of In[1]:= p1 20570064
During evaluation of In[1]:= ReplaceAll::reps: {<<1>>} is neither a \
list of replacement rules nor a valid dispatch table, and so cannot \
be used for replacing. >>
During evaluation of In[1]:= p2 10720384
During evaluation of In[1]:= Part::partw: Part 1922 of u[delt] does \
not exist. >>
During evaluation of In[1]:= Part::partw: Part 2 of u[delt] does not \
exist. >>
During evaluation of In[1]:= Part::partw: Part 1923 of u[delt] does \
not exist. >>
During evaluation of In[1]:= General::stop: Further output of \
Part::partw will be suppressed during this calculation. >>
During evaluation of In[1]:= $RecursionLimit::reclim: Recursion depth \
of 256 exceeded. >>
During evaluation of In[1]:= $RecursionLimit::reclim: Recursion depth \
of 256 exceeded. >>
During evaluation of In[1]:= $RecursionLimit::reclim: Recursion depth \
of 256 exceeded. >>
During evaluation of In[1]:= General::stop: Further output of \
$RecursionLimit::reclim will be suppressed during this calculation. >>
[... Computation aborted ...]
> It would be great if I could get a solution for this!!
The best thing to do is to post a fully working example that closely
match your problem, so people can reproduce the errors and try to fix them.
Regards,
--
Jean-Marc
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