legendrefdnum is a Python 2.x module for solving Sturm-Liouville problems of the type
![-\frac{d}{d x}\left[(1-x^{2})\frac{d u(x)}{d x}\right]+q(x)u(x)=\lambda u(x),\quad x\in(-1, 1),](/imathsoft/legendrefdnum/blob/master/images/eq1.png)
It has been proved to be exponentially convergent for
The module was developed based on the algorithm published in the article Volodymyr L. Makarov, Denys V. Dragunov, Danyil V. Bohdan. Exponentially convergent numerical-analytical method for solving eigenvalue problems for singular differential operators. A preprint of this article is available from http://arxiv.org/abs/1309.5795.
legendrefdnum comes extensively commented and with example code. You don't have to understand the FD-method to use legendrefdnum.
The following modules are mandatory dependencies: numpy, scipy, matplotlib. Having mpmath installed is optional but highly recommended for calculations with dense meshes (see legendrepqwrappers.py for an explanation).
To run legendrefdnum on Ubuntu 12.04 or later do the following:
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Clone the GitHub repository.
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Execute the command
sudo apt-get install python-numpy python-scipy python-mpmath python-matplotlibin the terminal. -
Run
example1.pyfrom the cloned repository to make sure everything works.
GNU LGPLv2.1+