f'[t]== x[t]+u[t] ?

*To*: mathgroup at smc.vnet.net*Subject*: [mg51580] f'[t]== x[t]+u[t] ?*From*: ames_kin at yahoo.com (ames kin)*Date*: Sat, 23 Oct 2004 00:22:30 -0400 (EDT)*Sender*: owner-wri-mathgroup at wolfram.com

I was thinking about solving that using Mathematica. Clearly I do not have enough math background. I wanted to get some feedbacks from the group. let, f'[t]== x[t]+u[t] where u[t] is the noise term. or fluctuation term. When you have a system with noise present, ( as in stochastic ode) is it Ok or acceptable to obtain the deterministic solution in the form of Mathematica InterpolatingFunction, and then add the noise when you Evaluate the InterpolatingFunction. ie, << Graphics`Colors` << Graphics`Graphics` sol = NDSolve[{Derivative[3][y][x] + Derivative[2][y][x] + Derivative[1][y][x] == -y[x]^3, y[0] == 1, Derivative[1][y][0] == Derivative[2][y][0] == 0}, y, {x, 0, 20}]; which outputs an interpolating function which has to be "evaluated" before it can be plotted. If so, If I throw in fluctuation as one Table the evaluation, it will have an appearance of wide fluctuation. so, Table[Evaluate[y[x] /. sol[[1]]] + Random[Real, {-0.3, 0.3}], {x, 0, 20, 0.2}] which then can be plotted. ListPlot[Table[Evaluate[y[x] /. sol[[1]]] + Random[Real, {-0.3, 0.3}], {x, 0, 20, 0.2}], PlotStyle -> {GrayLevel[0.8]}, PlotJoined -> True, PlotRange -> All, Axes -> False, Frame -> True, DisplayFunction -> Identity]; What is wrong with this method of solution for a system such as f'[t] == x[t] + u[t] ? (where u is the noise. this is my, most likely erroneous, interpretation of stochastic ode) I mean, what is wrong with this method mathematically. thanks in advance for any feedback from the group.