tautoolbox 0.95.0

A package that implements Lanczos' Tau method to solve differential problems

Tau Toolbox

AUTHORS:

   Paulo B. Vasconcelos
   Centro de Matemática - Universidade do Porto
   Email: [e-mail]

   José M. A. Matos
   Centro de Matemática - Universidade do Porto
   Email: [e-mail]

   José A. O. Matos
   Centro de Matemática - Universidade do Porto
   Email: [e-mail]

   Nilson Lima

REFERENCE:

   Solving differential eigenproblems via the spectral Tau method
   NUMERICAL ALGORITHMS
   DOI: https://doi.org/10.1007/s11075-022-01366-z

SOFTWARE REVISION DATE:

   Version 0.95 : 2025-04-10

Tau Toolbox is a Python library for the solution of integro-differential problems based on the Lanczos' Tau method.

Tau Toolbox is free software released under the GNU Lesser General Public License version 3 (LGPLv3). A copy of the License is enclosed in the project.

Installation

Just clone the Tau Toolbox repository following git clone https://bitbucket.org/tautoolbox/taupy.git.

Tau Toolbox can also be obtained at https://cmup.fc.up.pt/tautoolbox/.

Tautoolbox requires Python 3.10 together with the following modules:

• numpy
• matplotlib

Help

A Tau Toolbox User Guide will be made available soon, along with a set of Technical Reports.

Support

The project supports the tool in the sense that reports of errors or poor performance will gain immediate attention from the developers.

Getting started

The best way to get started is by using the many examples provided.

Tackle your problems with ease:

• To solve the ordinary differential problem $y''(x)+y(x)= 0$ in $[0,2\pi]$ with $y(0)=1$ and $y'(2\pi)=0$, just type:

import tautoolbox as tau
import numpy as np
from tautoolbox.functions import diff, linspace
import matplotlib.pyplot as plt

equation = lambda x, y: diff(y, 2) + y
domain = [0, 2 * np.pi]
conditions = lambda y: [y(0) - 1, y.diff(1, 2 * np.pi)]
problem = tau.problem(equation, domain, conditions)
yn = tau.solve(problem)[0]

x = linspace(yn)
plt.plot(x, yn(x))
plt.show()

You can find more examples in the examples folder.

Notice that we refer sometimes to taupy, this is not to be confused with the taupy package. This reference, that we have used internally since 2021, refers to the Python implementation of the Matlab/Octave Tautoolbox. There are some small differences between both implementations but the general structure is the same, and as long as possible, the syntax is also the same adapted to the syntax of each language.