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
IEE S.A.
ZAE Weiergewan
11, rue Edmond Reuter
L-5326 Contern
Luxembourg
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