       Re: Operations on InterpolatingFunction

• To: mathgroup at smc.vnet.net
• Subject: [mg100855] Re: Operations on InterpolatingFunction
• From: dh <dh at metrohm.com>
• Date: Tue, 16 Jun 2009 21:52:04 -0400 (EDT)
• References: <h0t846\$r6n\$1@smc.vnet.net>

```
Hi Porscha,

obviously there are only rules to integrate InterpolatingFunctions but

none for functions of InterpolatingFunctions.

You could add such rules, but it is easier to write the "function of a

InterpolatingFunction" as an InterpolatingFunction.

ifun2 = FunctionInterpolation[ifun[x]^2, {x, 0, Pi}]

Now you can integrate ifun2:

Integrate[ifun2[t], t]

hope this helps, Daniel

Porscha Louise McRobbie wrote:

> Hi,

>

> Solving a simple differential equation:

> ifun = First[

>    u /. NDSolve[{u''[t] + u[t] == 0, u == 0, u' == 1},

>      u, {t, 0, \[Pi]}]]

>

> returns the InterpolationFunction object, as expected. I can integrate

> this function (and obtain another InterpolatingFunction to be plotted,

> etc.) by:

>

> Integrate[ifun[t], t]

>

> 1. Why doesn't the following produce an InterpolatingFunction in the same way?

>

> Integrate[ifun[t]^2, t]

>

> 2. How can I normalize the solutions found using NDSolve?

> Norm[ifunt[t]] doesn't work...

>

> Thanks for any help.

>

>

>

>

>

>

```

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