NDSolve is not deterministic in its solutions??

*To*: mathgroup at smc.vnet.net*Subject*: [mg129321] NDSolve is not deterministic in its solutions??*From*: JBB <barandiaran.juan at gmail.com>*Date*: Wed, 2 Jan 2013 21:15:47 -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

I have a NDSolve in Mathematica 8 .0.1 in which I want to extract (with Sow) the maximums and minimums and also stop the integration when the maxima of the oscillation is under a threshold. Both conditions require \[Alpha]'[t]==0. The issue I find is that if I execute the same line of code several times, sometimes it records the last maxima and sometimes it doesn't. Is there a way to avoid this non deterministic behaviour in NDSolve? I solved it checking later if the last maxima is in the list and if it is not, adding it in another line of code, but this doesn't look a "nice" solution. Here is the code: Module[{interp, tmaxTemp, surf}, surf = 0.162; Label[repeatChangingSurface]; (*If NDSolve has errors returns here \ and tries again with a slightly different surface *) tmaxTemp = 1000;(* Define a long enough time of integration to ensure \ convergence *) interp = FlattenAt[ (*Eliminate unneccesary nestings in the list result *) Reap[Quiet@ NDSolve[{1.1089 \[Alpha]''[t] + 1.2936 Sin[\[Alpha][t]] + 210*surf* (0.33 Sin[\[Alpha][t]] + ( 0.33^2 Cos[\[Alpha][t]] Sin[\[Alpha][t]])/Sqrt[ 1 - 0.33^2 Sin[\[Alpha][t]]^2]) * UnitStep[Sin[\[Alpha][t] + Pi*UnitStep[-\[Alpha]'[t]]]] == 0, \[Alpha][0] == -Pi/3, \[Alpha]'[0] == 0}, \[Alpha], {t, 0, tmaxTemp}, Method -> {"EventLocator", "Event" -> {\[Alpha]'[t], \[Alpha]'[t]}, "EventCondition" -> {True, (Abs[\[Alpha][t]] < 0.01)}, "EventAction" :> {Sow[{t, \[Alpha][t], surf}], Throw[tmaxTemp = t, "StopIntegration"]}}]], {{1}, {2}}]; If[tmaxTemp == interp[[1]][[1]][[2]][[1]][[1]][[2]],(* If tmaxTemp is the same as the last value of the interp function, the NDSolve has finished succesfully*) interp, surf = surf*1.0001; Goto[repeatChangingSurface];] (* Else there was an error in NDSolve \ and we try with a sligthly different surface *) ] Notice that if you repeat the execution several times the list of maxima changes. Sometimes you get this result: {{\[Alpha] -> \!\(\* TagBox[ RowBox[{"InterpolatingFunction", "[", RowBox[{ RowBox[{"{", RowBox[{"{", RowBox[{"0.`", ",", "7.578028259624528`"}], "}"}], "}"}], ",", "\<\"<>\"\>"}], "]"}], False, Editable->False]\)}, {{1.97478, 0.283895, 0.162}, {3.84739, -0.0799267, 0.162}, {5.71299, 0.0225631, 0.162}, {7.57803, -0.00637085, 0.162}}} and sometime this other: {{\[Alpha]->InterpolatingFunction[{{0.,7.57803}},<>]},{{1.97478,0.283895,0.162},{3.84739,-0.0799267,0.162},{5.71299,0.0225631,0.162}}}