       Re: Calculations with Interpolating Functions

• To: mathgroup at smc.vnet.net
• Subject: [mg88532] Re: Calculations with Interpolating Functions
• From: dh <dh at metrohm.ch>
• Date: Wed, 7 May 2008 07:10:48 -0400 (EDT)
• References: <fvpcqn\$mhn\$1@smc.vnet.net>

```
Hi Joao,

you can always re-interpolate a function of an interpolating function.

Therefore, write  your function Sin[...] as an interpolationg function.

Here is an example:

t=FunctionInterpolation[x^2,{x,0,2}];

ts=FunctionInterpolation[Sin[t[x]],{x,0,2}];

Integrate[ts[x],{x,0,2}]

hope this helps, Daniel

João Paulo Casquilho wrote:

> Hi

>

>

>

> I obtain an Interpolating function as a solution of a differential equation

> with the command NDSolve, lets call it =93solution=94, which gives x(t). Next I

> want to use this solution for further calculations. With the commands

> =93result=Evaluate[x(t)/. First[solution]]=94 or =93result=  x(t)/.solution,

> {t,0,tmax}=94 I do the plot x(t) without any problems. Now, with version 5.2 I

> manage to integrate x(t) or linear functions of it.  But when I try to

> integrate non linear functions of x(t), like x(t)^2 or Sin[x(t)] (which is

> what I want),  Mathematica is unable to give a numerical result, all I get

> is an integral saying that there is an InterpolatingFunction in the

> integrand. With Mathematica 6 the linear integration does not work either.

>

> Any help would be appreciated.

>

>

>

> Best Regards

>

>

>

> Joao Paulo

>

>

>

```

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