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Re: Problems integrating InterpolatingFunction

• To: mathgroup at smc.vnet.net
• Subject: [mg116050] Re: Problems integrating InterpolatingFunction
• From: Gary Wardall <gwardall at gmail.com>
• Date: Sun, 30 Jan 2011 03:32:47 -0500 (EST)
• References: <ii2c82$ra6$1@smc.vnet.net>

On Jan 29, 6:43 pm, Sergio Miguel Terrazas Porras <sterr... at uacj.mx>
wrote:
> Hello group,
>
> I use NDSolve for a nonlinear differential equation, and I get an InterpolatingFunction, as expected.
>
> I can plot it, evaluate it, etc.
>
> The problem I have is that now I need to integrate 1/(the square of the InterpolatingFunction), and I get nothing but the input back.
>
> Any ideas?
>
> Thanks in advance.
>
> Sergio Terrazas

I'm a bit rusty with my ODE theory but you might try restating your
problem in terms of a system of ODE's.

Suppose:

y1=92=f(x)      &   f(x0)=y10       (The function you used with NDSolve
on originally.)

With:

y2=Integral( 1/(f(x)^2 )         (The function you really want at the
end.)


So:

y2=92=1/(y1)^2


Then the system to solve would be:


y1=92=f(x)               &    y1(x0)=y10

y2=92=1/(y1)^2      &     y2(x0)=0

I hope this or a some variation should be of some help.

Gary Wardall