dborzov / fredholm

Solves integral equations with singular divergences numerically

=========== Fredholm.py

Fredholm python package allows you to solve integral equations numerically.

See dborzov.github.io/fredholm for more details.

Fredholm's integral equation of the first order can be written in the following way::

    int K(y,x) phi(x) dx = f(y)

To use it, define the Fredholm's integral kernel of the equation and the nonhomogenious term::

    #!/usr/bin/env python

    import Fredholm
    Fredholm.Kernel = lambda x,y: 1/(x**2 + y**2)
    Fredholm.f = lambda x: 1.
    Fredholm.range.low, Fredholm.range.high = 0. , 100.
    Fredholm.solve()
    print Fredholm.solution(2.) 

Fredholm.solution yeilds the NumPy interpolation function that is defined in the defined range.

Features

Here are some reasons to know and love Fredholm:

1. The adaptive integration mesh

2. Can take care of principal value integrals