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Re: NDSolve

Jim McGuire wrote:
> I have been using NDSolve to successfully solve some differential
> equations and would like to export the interpolating functions to some
> compiled C/Fortran code.  Is there a straightforward way of doing this?

An InterpolatingFunction is an object which encapsulates the data
produced by the ODE solver run by NDSolve, and it is quite simple to
export the data.  However, what would be very difficult to export would
be the ability to evaluate the InterpolatingFunction object at an
argument -- i.e. its role as an approximate function.  (The code for
evaluating these is of course based on piecewise polynomial
interpolation methods and is moderately complex.)

If you want the data, the third part of an InterpolatingFunction object
is the grid (or knots) at which data values are defined, and the fourth
part is the actual data (possibly including derivatives).  Here is a
simple example:

In[1]:= fun = x /. First[NDSolve[{x'[t] == x[t],x[0] == 1},x,{t,0,.1}]]

Out[1]= InterpolatingFunction[{{0., 0.1}}, <>]

These are the points at which data is defined:

In[2]:= fun[[3]]

Out[2]= {{0., 0.0000998752, 0.00019975, 0.0207957, 0.0413916, 0.0619875,

This is enclosed in an extra {} because an InterpolatingFunction object
may be multidimensional -- then outer {} contains the list of values
for each dimension.

This gives the data (including derivative values) corresponding to the
points above

In[3]:= fun[[4]]

Out[3]= {{1.}, {1.0001, 1.0001}, {1.0002, 1.0002, 0.5001},

>    {1.02101, 1.02101, 0.505303}, {1.04226, 1.04226, 0.515818},

>    {1.06395, 1.06395, 0.526553, 0.173737},

>    {1.10517, 1.10517, 0.554975, 0.224068}}

The data is arranged in lists of increasing order, and derivatives are
divided by the factorial of the order.  Thus, at t == 0.1, we have {f,
f', f''/2!, f'''/3!} == {1.10517, 1.10517, 0.554975, 0.224068}

Be warned, however, that the internal format of data objects like this
may change from version to version.  In the next release of
Mathemematica that will be coming out there will be a change in the
format of the data to take advantage of more compact storage, but with
only slightly more effort, you could still get this information.

Rob Knapp
Wolfram Research

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