Hello,

Introduction
Let me introduce myself first.
I'm Lawrence Mulholland and I'm Group Leader for a Group called
"Numerical Libraries" which includes a large proportion of our
internal developers. I look after project development as we move
from one major release of the Library based products to the next;
so I am currently managing a FL23 project which aims to produce
its first implementations of FL23 at the latter part of this year.

Painleve Equations

I have recently been invited to a workshop hosted by ICMS in Edinburgh on Painleve equations: http://icms.org.uk/workshops/painleve

This seems like an interesting area of research; and since we are looking to introduce a routine for the Hypergeometric function 2_F_1 in FL23, it seems like a logical extension to be investigating the even more challenging Painleve equations which seem to have a fair range of applications.

What I'm not sure about is: how useful would routines that provide particular solutions to the Painleve equations be to our customer base and to the research community in particular ?

Does anyone out there have any interest in this?

Lawrence

I've never heard of them to be honest. What sort of applications do they have?

ReplyDeleteI'm new to these too.

ReplyDeleteThe objectives set out for the Edinburgh Workshop states the following:

"people are finding that the solutions to an extraordinarily broad array of scientific problems, from neutron scattering theory, to PDEs, to transportation problems, to combinitorics, etc, can be expressed in terms of Painleve transcendents."

One of the main driving forces of the research in this area seems to be Professor Peter Clarkson at the University of Kent:

http://www.kent.ac.uk/ims/staff/pac3/

I have started by reading his lengthy presentation:

http://www.ima.umn.edu/talks/workshops/7-22-8-2-2002/clarkson/SF02L.ps

I found the relation to soliton solutions of well-known nonlinear wave equations illuminating.

Dear Lawrence,

ReplyDeleteI'm also attending the workshop.

Thanks for the link to Clarkson's slides.

Folkmar Bornemann has done lovely recent work using Fredholm determinants to evaluate PDFs arising in random matrix theory that are usually evaluated via Painleve ODEs:

http://arxiv.org/abs/0904.1581

So, random matrices (which have lots of apps in quantum physics and statistics) are the main area I have come across Painleve. But, I think we'll enjoy learning some other connections we didn't know about...

Cheers, Alex

Thanks Alex for the addition information.

ReplyDeleteOne of the reasons I will be there is to find out about the application areas for these equations. The more areas there are the more I can build up a case for NAG getting involved in collaborative projects on developing library grade software in this field.