D and InterpolatingFunction

• To: mathgroup at yoda.physics.unc.edu
• Subject: D and InterpolatingFunction
• From: TDR at vaxc.cc.monash.edu.au
• Date: 25 Jun 1993 13:57:34 +1100

```Pekka Janhunen asks:
>How does D handle interpolating functions? This would be extremely useful,
>but I haven't been able to find out how.. is it a new feature in 2.2?

InterpolatingFunction's are returned by several commands including NDSolve[],
and being able to differentiate them is indeed very useful. The feature was
there even in 2.0 I think.

In[1]:= ans=NDSolve[{y''[t]==Sin[y[t]], y[0]==Pi/4, y'[0]==0}, y, {t,0,10}][[1]]
Out[1]= {y -> InterpolatingFunction[{0., 10.}, <>]}

In[2]:= Plot[ Evaluate[y[t] /. ans], {t,0,10} ]
Out[2]= -Graphics-

In[3]:= Plot[ Evaluate[y'[t] /. ans], {t,0,10} ]
Out[3]= -Graphics-

In[4]:= Plot[ Evaluate[y''[t] - Sin[y[t]] /. ans], {t,0,10} ]
Out[4]= -Graphics-

Also D[y[t] /. ans, t] etc works too.

Terry Robb

```

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