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Re: Operations on InterpolatingFunction

  • To: mathgroup at smc.vnet.net
  • Subject: [mg100889] Re: Operations on InterpolatingFunction
  • From: Alexei Boulbitch <Alexei.Boulbitch at iee.lu>
  • Date: Wed, 17 Jun 2009 04:45:13 -0400 (EDT)

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.


Dear Porsha,
It seems that the built-in function Norm does not apply to integrals, does it?
Why not to define a norm that you need. Say, you need the Hilbert norm on your interval {0,Pi}:


ifun = First[
  u /. NDSolve[{u''[t] + u[t] == 0, u[0] == 0, u'[0] == 1},
    u, {t, 0, \[Pi]}]];

f=Function[x,ifun[x]];

In[43]:= a = NIntegrate[f[x]^2, {x, 0, Pi}];  (* This is the square of the norm *)

fn[x_] := f[x]/Sqrt[a];                       (* This is the normalized function *)


NIntegrate[fn[x]^2, {x, 0, Pi}]                (* this is control *)

Out[45]= 1.

Have fun and success, Alexei

-- 
Alexei Boulbitch, Dr., habil.
Senior Scientist

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