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MathGroup Archive 2002

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Re: Inv.Interpol.Function

  • To: mathgroup at smc.vnet.net
  • Subject: [mg36720] Re: Inv.Interpol.Function
  • From: Erich Mueller <emueller at mps.ohio-state.edu>
  • Date: Fri, 20 Sep 2002 04:16:40 -0400 (EDT)
  • Organization: Ohio State University
  • References: <am95s4$k3d$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

A slick way to solve this particular problem is to use NDSolve.  The
inverse function t[y] sattisfies the differential equation

t'[y]==1/R[t[y]]^4

with the inital condition

t[0]==0

So the following command should give an interpolating function for t[y]
(you should change the 1 in {y,0,1} to whatever the appropriate value is)

NDSolve[{t'[y]==1/R[t[y]]^4,t[0]==0},t,{y,0,1}]

Erich

On Wed, 18 Sep 2002, martin skogstad wrote:

> Dear NG
>
>
> Mabye this is too simple, but I cant just figure it out
>
> I want to get an inverse function for y[t] where
>
> y[t_]:=NIntegrate[R[x]^4,{x,0,t}] /. ndsolution[[1]]
> and
> R[t] is an interpolatingfunction(R>0 from NDSolve) on the interval 0=<t=<T
>
> after that I hope to be able to calculate the integral :
>
> a = (1/y[T])*
>         NIntegrate[R[InvFunction[y[t]]*Cos[y[t]], {y[t], 0, y[T]}]
>
> it works with a constant instead of R[t].
>
> Hope you can help, and that the above is understandable.
>
>
> Martin Skogstad
>
>



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