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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.

E.g. your case:

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] == 0, u'[0] == 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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