A Mathematica package for computing solutions to matrix-valued Riemann–Hilbert problems.
Examples include computing Cauchy and Hilbert transforms, homogeneous Painlevé II (such as the Hastings–McLeod solution and Ablowitz–Stegun solutions for large x), Painlevé III and Painlevé IV.
Includes a routine for evaluating Painlevé II:
evaluates the solution to Painlevé II with Stokes' constants s1, s2 and s3 at the point x. The computation is reliable for all real x.
The software was developed by Sheehan Olver with contributions from Georg Wechslberger, based on the framework described in Found. Comput. Maths, 11: 153–179 and a paper to appear in Numer. Math.
To use, download the package:
alpha version 0.4, 4 Feb 2011.
Then follow the installation instructions in the file INSTALL.nb.
The current (untested) version of the code is available from the
is included with permission from Michael Prahofer and Herbert Spohn, and is available online. All other files are © Sheehan Olver, 2010, subject to a BSD license.
The package includes contributions from Georg Wechslberger.