NumericalUniversality
NumericalUniversality is a Mathematica library that contains a database, algorithms and random matrix distributions for examining two-component universality in the halting times for these algorithms.
NumericalUniversality Repository
A full wiki article is available above to describe the use of the package.
NumericalUniversality Repository
A full wiki article is available above to describe the use of the package.
Two-component universality in the QR eigenvalue algorithm
ISTPackage
ISTPackage is a Mathematica package that contains various routines for effectively evaluating the inverse scattering transform. Thus far it has been implemented for the Korteweg-de Vries (KdV) equation, the focusing and defocusing modified KdV equations and the focusing and defocusing nonlinear Schrödinger (NLS) equations. It also contains a routine for the linear Schrödinger equation. The code can be found on bitbucket:
ISTPackage Repository
The package allows for the computation of highly oscillatory solutions. The animation below includes a picture-in-picture evolution of a solution of the KdV equation. The animation tracks both the dispersive tail moving to the left and the solitons moving to the right.
ISTPackage Repository
The package allows for the computation of highly oscillatory solutions. The animation below includes a picture-in-picture evolution of a solution of the KdV equation. The animation tracks both the dispersive tail moving to the left and the solitons moving to the right.
A highly oscillatory solution of the KdV equation
Hill's Method
The following is a Python-based implementation of Hill's method. The software includes a GTK-based GUI. This project is no longer being maintained.
Hill's Method in Python
Hill's Method in Python