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From: Frederick Akalin (akalin_at_[hidden])
Date: 2006-07-31 23:38:14

"Numerical integration" is often loosely used to mean quadrature, ODE
solving, and PDE solving. I was just following the terminology on
the Wiki; I'm sorry if I wasn't clear.

I was talking about ODE solving in my original e-mail, but of course
there might be a need for PDE solving and quadrature libraries, too.
That PDE library looks interesting, although I don't have much
experience with solving PDEs. It looks like a bunch of people have
quadrature routines, too, so it might be beneficial to integrate that
into a coherent library.

Anyway, I hacked up an example program demonstrating what I'm talking
about, available at: ,
which should be compilable by itself. The interesting stuff is the
classes at the top. Some notes:

- The step routines are taken straight out of a numerical analysis
reference. Note that they are completely container-agnostic, so they
can be used with floats, vectors of floats, vectors of particles
which have their own floats, etc. Other libraries are more
restricted. For example, the GSL library routines only work with
double arrays:
Equations . Also, the ODE++ library (
www/fakultaet/iam/ode++/ode++_e.html#Problem ) requires adapting your
code to their framework, including using their vector/matrix classes.
(I only took a cursory look at the documentation -- correct me if I'm
misrepresenting anything)
- I haven't done any performance tests, but it seems to me that a
reasonably smart container/adapter (with expression templates) would
incur only a small performance hit compared with hand-coded C or
Fortran. (Tell me if I'm dreaming :) )
- The member functions are templated instead of the classes
themselves. That's just for convenience, as more sophisticated
steppers (ones that store state) probably need to be class-
templated. I also omitted a Jacobian parameter for simplicity, as
these solvers don't need them.
- A real ODE-solver library would of course include higher-level
drivers for different types of adaptive stepping. Also, it would
probably include adaptors for common containers (Blitz++ vectors, etc.)
- I didn't test this example program thoroughly, so let me know if
you spot any errors.

Has anything like this been done before? I have a hard time
believing that such a simple idea would go unnoticed, even though my
own searches turned up nothing.


On Jul 31, 2006, at 8:46 AM, Sohail Somani wrote:

> I'm unsure what ODE's have to do with integrals.
> Anyway, for solving PDEs one should look at
> index.
> html for an example.
> I'd be interested to know if anyone has used this library :)
> Sohail
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