.. role:: func(code)

Solve Volterra and Fredholm integral equations

|Volterra plot generated by package|

.. docs-start

This Python package estimates Volterra and Fredholm integral equations using known techniques.

Installation

This package can be installed with pip::

pip install inteq

and can be upgraded using the --upgrade flag::

pip install --upgrade inteq

Supported Equations

Volterra ^^^^^^^^

|Volterra plot generated by package|

This package provides the function :func:inteq.SolveVolterra which approximates the solution, g(x), to the Volterra Integral Equation of the first kind:

|vie|

using the method in Betto and Thomas (2021) <https://mattwthomas.com/papers/asymmetric-all-pay-contests-with-spillovers/>__.

Fredholm ^^^^^^^^

|Fredholm plot generated by package|

This package provides the function :func:inteq.SolveFredholm which approximates the solution, g(x), to the Fredholm Integral Equation of the first kind:

|fie|

using the method described in Twomey (1963) <https://doi.org/10.1145/321150.321157>__. It will return a smooth curve that is an approximate solution. However, it may not be a good approximate to the true solution.

.. |Volterra plot generated by package| image:: https://raw.githubusercontent.com/mwt/inteq/main/docs/volterra/volterra-example.svg .. |vie| image:: https://latex.codecogs.com/svg.latex?\large&space;f(s)=\int_a^sK(s,y)g(y)dy :alt: f(s) = \int_a^s K(s,y) g(y) dy .. |Fredholm plot generated by package| image:: https://raw.githubusercontent.com/mwt/inteq/main/docs/fredholm/fredholm-example.svg .. |fie| image:: https://latex.codecogs.com/svg.latex?\large&space;f(s)=\int_a^bK(s,y)g(y)dy :alt: f(s) = \int_a^b K(s,y) g(y) dy