https://github.com/dlfivefifty/RHPackage

A Mathematica package for solving Riemann–Hilbert problems numerically
https://github.com/dlfivefifty/RHPackage

Last synced: about 1 month ago
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A Mathematica package for solving Riemann–Hilbert problems numerically

• Host: GitHub
• URL: https://github.com/dlfivefifty/RHPackage
• Owner: dlfivefifty
• Created: 2011-11-30T02:47:41.000Z (about 13 years ago)
• Default Branch: master
• Last Pushed: 2019-07-23T09:14:40.000Z (over 5 years ago)
• Last Synced: 2024-10-13T22:34:45.464Z (2 months ago)
• Language: Mathematica
• Homepage: http://www.maths.usyd.edu.au/u/olver/projects/RHPackage.html
• Size: 4.22 MB
• Stars: 26
• Watchers: 9
• Forks: 12
• Open Issues: 4
• Metadata Files:
  • Readme: README.md

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README

        
# RHPackage

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:

```mathematica

	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

# Installation instructions

Download the repository and follow the installation instructions in the file INSTALL.nb.

# 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.