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How do you update variables in NDSolve for each step?

  1. May 22, 2012 #1
    Im using NDSolve. I need to be able to update a variable inside NDSolve each time NDSolve takes a step. "rand" is the variable I want to update each step. I want it to be a different number each step. The below is an example that illustrates what I have currently happening ("rand" does not update for each step).
    Code (Text):

    rand=RandomReal[]
    Solution = y /. Flatten[ NDSolve[{y'[x] == .25 rand, y[0] == 1}, y, {x, -10, 10}]]
    Plot[Evaluate[Solution[x]], {x, -10, 10}, PlotRange -> {-1.5, 1.5}]
     
    Instead of picking 1 random variable for "rand" for the entire x domain, I want "rand" to be different for each step i.e. a different "rand" for x=1, x=2, x=3, etc.
     
    Last edited: May 22, 2012
  2. jcsd
  3. May 22, 2012 #2
    When you say each step, do you mean each step in x i.e step in the internal integration?

    If so then the only way I can think of at the moment (not even sure if this is what you want) is to generate a table of random points, each associated with an x value and parse that as a function of x, i.e.

    y'[x] = 0.25 f(x) where f(x) maps to your interpolated random set.
     
  4. May 22, 2012 #3
    yes, when i say step i mean each step in x inside of NDSolve.

    I think i may have found an answer to this. Im posting it incase anyone else should ever find this and need help.

    The ?NumericQ prevents the expression simply getting replaced by RandomReal[].

    rand[x_?NumericQ] := RandomReal[];
    Solution = y /. Flatten[NDSolve[{y'[x] == .25 rand[x], y[0] == 1}, y, {x, -10, 10}, PrecisionGoal->0]]
     
  5. May 22, 2012 #4
    You could also probably wrap it in an Evaluate[].
     
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