integrate an interpolated function

• To: mathgroup at smc.vnet.net
• Subject: [mg70294] integrate an interpolated function
• From: wtplasar at ehu.es
• Date: Thu, 12 Oct 2006 05:36:55 -0400 (EDT)

```Hi,

I have defined numerical derivatives of functions by interpolation,
because for some complicated numerical functions I was getting
convergence problems using ND.

I have defined the second derivative of a 2 variable function by
interpolating the function in a square region with the point where I
want to evaluate the function at its center. I do it here for Sin[x*y]
as an example.

yyder[om_?NumericQ,
w_?NumericQ, h_?NumericQ] := D[FunctionInterpolation[Sin[x*y],
{x, om - \
h, om + h}, {y, w - h, w + h}][x, y], {y, 2}] /. x -> om /. y -> w

Then I want to perform an operation on this function which involves
integrating it over one of the variables (multiplying it by another
function, but that does not matter).

So I do

fun[w_?NumericQ, h_?NumericQ] := NIntegrate[yyder[om, w, h], {om, 0,
1}]

and I get a series of errors like:

FunctionInterpolation::range: Argument {x, om - 0.3, om + 0.3} is not
in the
form of a range specification, {x, xmin, xmax}.

FunctionInterpolation::range: Argument {#2, #3, #4} is not in the form
of a
range specification, {x, xmin, xmax}

and so on.

Can you help me? Thanks,

Ruth

```

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