I'm trying to introduce a randomized element in a simulation, using NDSolve to do the integration. The random element is supposed to simulate a random thermal force. The way I've tried to implement this is by creating an array of random values and then trying to select values from the array during each time step. The following is a snippet of my current code.
(*Initialising some time values that will allow me to select particular values from my random array*)
Tfinal = 10;
SampleFreq = 2500;
NoT = Tfinal*SampleFreq + 1;
dt = Tfinal/(NoT - 1);
(*Array of random values and the function I'll be using in NDSolve*)
WN = RandomVariate[NormalDistribution[0, 1], NoT];
WNoise[t_] := Indexed[WN, Floor[Floor[t/dt]] + 1]
(*NDSolve function using white noise function*)
sol = x[t] /.
NDSolve[{D[x[t], t, t] == -(w^2) x[t] + WNoise[t], x[0] == 0,
x'[0] == 2 }, x, {t, 0, 10}]
The function above (without white noise) is the classic F = -kx equation. I've just tried to introduce a white noise driving force force to it as well. Unfortunately, it doesn't work when the WNoise function is added. The error message I typically get is the following.
Indexed::ind: The index 1/2 is not a nonzero integer.
NDSolve::ndnum: Encountered non-numerical value for a derivative at t == 0.`.
I'm just wondering if anyone has faced a similar problem and if this method of introducing white noise is possible or if I'm just being silly with this implementation.
Thank you for your help.
