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Re: NDSolve very very slow
Posted:
Oct 25, 2012 11:34 PM
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Bob Hanlon and others may have suggestions to speed things up, but note
that you are doing your calculations with 40 place precision. Since it
is not machine precision, this significantly impacts the speed. How
would you do a 40-place calculation in C++?
Kevin
On 10/25/2012 1:41 AM, popov.ghost@gmail.com wrote:
> M=1;
> \[Lambda][l_] = l (l + 1);
> rinf = 15000;
> $MinPrecision = 40;
> wp = $MinPrecision;
> ac = $MinPrecision - 8;
> pg = wp/2;
>
> eq[\[Omega]_,
> l_] := \[CapitalPhi]''[r] + (2 (r - M))/(
> r (r - 2 M)) \[CapitalPhi]'[
> r] + ((\[Omega]^2 r^2)/(r - 2 M)^2 - \[Lambda][l]/(
> r (r - 2 M))) \[CapitalPhi][r] == 0;
>
> (*The solution:*)
>
> \[CapitalPhi]out[\[Omega]_, l_] := \[CapitalPhi]out[\[Omega], l] = {\[CapitalPhi], \[CapitalPhi]'} /.
> Block[{$MaxExtraPrecision = 100},
> NDSolve[{eq[\[Omega], l], \[CapitalPhi][rinf] ==
> init, \[CapitalPhi]'[rinf] ==
> dinit}, {\[CapitalPhi], \[CapitalPhi]'}, {r, 29,
> 39}, WorkingPrecision -> wp,
> AccuracyGoal -> ac, PrecisionGoal -> pg,
> MaxSteps -> \[Infinity]]][[1]];
>
> (*Run as:*)
>
> \[CapitalPhi]out[2, 1]//AbsoluteTiming
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