Solve various integral equations using numerical methods in Python

Last update: Nov 28, 2022

Overview

Solve Volterra and Fredholm integral equations

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

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

$f(s) = \int_a^s K(s,y) g(y) dy$

using the method in Betto and Thomas (2021).

Fredholm

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

$f(s) = \int_a^b K(s,y) g(y) dy$

using the method described in Twomey (1963). It will return a smooth curve that is an approximate solution. However, it may not be a good approximate to the true solution.

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Comments

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Details

| File | Before | After | Percent reduction | |:--|:--|:--|:--| | /assets/volterra-example.svg | 26.30kb | 22.86kb | 13.07% | | /assets/fredholm-example.svg | 25.53kb | 22.25kb | 12.87% | | /assets/trap-vs-mid1.svg | 28.22kb | 24.66kb | 12.63% | | /assets/trap-vs-mid2.svg | 32.13kb | 28.27kb | 12.01% | | /assets/fredholm-equation.svg | 15.17kb | 14.71kb | 3.04% | | /assets/volterra-equation.svg | 15.24kb | 14.78kb | 3.03% | | | | | | | Total : | 142.60kb | 127.53kb | 10.57% |

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Releases(v0.2.0)

v0.2.0(May 9, 2021)

Fredholm equations are finally confirmed to be working.
Source code(tar.gz)
Source code(zip)
v0.1.2(May 8, 2021)

This release allows you to apply the trapezoid rule in a VIE.
Source code(tar.gz)
Source code(zip)

Owner

Matthew Wildrick Thomas

Economics PhD candidate at Northwestern University. Follow me!

GitHub Repository https://inteq.readthedocs.io

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Solve various integral equations using numerical methods in Python

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