# RHPackage

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:
PainleveII[{s1,s2,s3},x]

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.*
## Installation instructions

To use, download the package:

alpha version 0.4, 4 Feb 2011.

Then follow the installation instructions in the file INSTALL.nb.
## Repository

The current (untested) version of the code is available from the

RHPackage repository
## License

The file
RiemannHilbert/Data/McLeodSolution.txt

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.