How do you update variables in NDSolve for each step?

[xpress907]

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).

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.

 

[FunkyDwarf]

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.

 

[xpress907]

yes, when i say step i mean each step in x inside of NDSolve.

I think i may have found an answer to this. I am 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]]

 

[FunkyDwarf]

You could also probably wrap it in an Evaluate[].

 

[alphy]

To update a variable within NDSolve for each step, you can use the "WhenEvent" option. This option allows you to specify an event that will trigger a change in the variable value. In this case, we can use the "TimeStep" event which will trigger at each time step taken by NDSolve. The updated "rand" value can be generated within the "WhenEvent" function using RandomReal[].

Here is an example:

rand = RandomReal[];
Solution = y /. Flatten[NDSolve[{y'[x] == .25 rand, y[0] == 1,
WhenEvent[TimeStep[x], rand = RandomReal[]]}, y, {x, -10, 10}]];

Plot[Evaluate[Solution[x]], {x, -10, 10}, PlotRange -> {-1.5, 1.5}]

This will update "rand" at each time step and use the updated value in the differential equation. You can also specify different conditions for when the event should trigger, such as a specific time or value of the variable "x". For more information on the "WhenEvent" option, you can refer to the NDSolve documentation.