Re: Real time progress of NDSolve

*To*: mathgroup at smc.vnet.net*Subject*: [mg129711] Re: Real time progress of NDSolve*From*: Alexei Boulbitch <Alexei.Boulbitch at iee.lu>*Date*: Wed, 6 Feb 2013 05:51:59 -0500 (EST)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com*Delivered-to*: l-mathgroup@wolfram.com*Delivered-to*: mathgroup-newout@smc.vnet.net*Delivered-to*: mathgroup-newsend@smc.vnet.net

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, L-5326 Contern, LUXEMBOURG Office phone : +352-2454-2566 Office fax: +352-2454-3566 mobile phone: +49 151 52 40 66 44 e-mail: alexei.boulbitch at iee.lu