A Mathematica package for solving Riemann–Hilbert problems numerically
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 Numer. Math. 122: 305–340
Download the repository and follow the installation instructions in the file INSTALL.nb.
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.