Re: NDsolve with a quasi random scource

• To: mathgroup at smc.vnet.net
• Subject: [mg107631] Re: NDsolve with a quasi random scource
• From: David Bailey <dave at removedbailey.co.uk>
• Date: Sat, 20 Feb 2010 06:38:33 -0500 (EST)
• References: <hllibo\$o3\$1@smc.vnet.net>

```Clint Zeringue wrote:
> Hello,
>
> I have a quick question regarding the use of a pseudo-random scource inside NDsolve.
>
> Suppose you have the following:
>
> scource[z_,]:= RandomReal[{-5,5}]
>
> Then in NDsolve we have
>
> NDsolve[f'[z] + f[z] == scource[z],f,{z,0.5}]
>
> My question is as the integrator works to solve this system within NDsolve is it really putting in a random number at each z-step? or is it just evaluated scource[z] once and returning a number, and then going into the integrator?'
>
> Nevertheless, How can I keep the algorithm that is actually solving this system to pull random numbers at each z step?
>
> Thanks,
>
> -Clint
>
You really don't want to think about z-steps when you use NDSolve,
because NDSolve will use whatever size steps it wants, and it really
requires that your function be consistent and preferably continuous :)

This problem crops up in simpler contexts than NDSolve, for example, it
makes no sense to plot a function such as:

Plot[Sin[z]+Random[],{z,0,10}]

because the 'frequency' of the random fuzz introduced will depend on the
step size that Plot uses.

You really need to think a bit more about what your function really is -
perhaps you should create a list of equally spaced random points, and
generate an interpolation between them to create your random source in a
step-independent way.

David Bailey
http://www.dbaileyconsultancy.co.uk

```

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