
Re: Real time progress of NDSolve
Posted:
Feb 6, 2013 5:51 AM


Hi all, Lately I'd been trying to solve some very complicated ODEs (they arise from modifications of General Relativity), but there were two problems: 1) NDSolve would take several (15+) minutes to solve them, 2) Many times it would actually fail as the system is very stiff. Trying to understand what was going on and also having a real time estimate of the progress of NDSolve, I came up with the following code that actually helped me address the issues mentioned above:
data = {{0, 1}}; k = 0; ProgressIndicator[Dynamic[k], {0, 30}] Dynamic[ListPlot[data, Frame > True, PlotRange > {{0, 31}, {0, 1.2}}]] NDSolve[{y'[x] == y[x] Cos[x + y[x]], y[0] == 1}, y, {x, 0, 30}, StepMonitor :> (Pause[.02]; Set[k, x]; AppendTo[data, {x, y[x]}])];
The ProgressIndicator provides the real time estimate of the progress and the Dynamic+ListPlot show where NDSolve has a certain "difficulty" (notice the "hiccup" in this example at x~12). The ODE used is of course very simple and not the one I used in practice.
In any case, this is not groundbreaking or anything, but it helped me and I thing it's quite cool, so I decided to share it.
Cheers
Hi, That's a nice example. I just would like to note that with advent of M9 there is a possibility to use also Gauges for the same purpose as the indicator. Makes the same, but looks less boring. Evaluate this:
Clear[x, y, data, k]; data = {{0, 1}}; k = 0; HorizontalGauge[Dynamic[k], {0, 30}] Dynamic[BulletGauge[k, 20, {0, 30}]] Dynamic[ListPlot[data, Frame > True, PlotRange > {{0, 31}, {0, 1.2}}]] NDSolve[{y'[x] == y[x] Cos[x + y[x]], y[0] == 1}, y, {x, 0, 30}, StepMonitor :> (Pause[.02]; Set[k, x]; AppendTo[data, {x, y[x]}])];
Have fun, Alexei
Alexei BOULBITCH, Dr., habil. IEE S.A. ZAE Weiergewan, 11, rue Edmond Reuter, L5326 Contern, LUXEMBOURG
Office phone : +35224542566 Office fax: +35224543566 mobile phone: +49 151 52 40 66 44
email: alexei.boulbitch@iee.lu

