Ecosyste.ms: Awesome

An open API service indexing awesome lists of open source software.

Awesome Lists | Featured Topics | Projects

https://github.com/lxvm/iteratedintegration.jl

Iterated h-adaptive integration (IAI)
https://github.com/lxvm/iteratedintegration.jl

Last synced: 10 days ago
JSON representation

Iterated h-adaptive integration (IAI)

Awesome Lists containing this project

README 

        
# IteratedIntegration.jl



| Documentation | Build Status | Coverage | Version |

| :-: | :-: | :-: | :-: |

| [![][docs-stable-img]][docs-stable-url] | [![][action-img]][action-url] | [![][codecov-img]][codecov-url] | [![ver-img]][ver-url] |

| [![][docs-dev-img]][docs-dev-url] | [![][pkgeval-img]][pkgeval-url] | [![][aqua-img]][aqua-url] | [![deps-img]][deps-url] |



This package provides experimental algorithms for globally h-adaptive iterated

integration.



The main takeaways of these experiments are that:

- pole-subtraction is superior to quadgk for integration of meromorphic functions

- The peak missing problem, which occurs for near singular functions, can be

  elegantly solved with auxiliary integrands

- nested integrals can be implemented reliably when absolute tolerances for

  inner integrals are scaled by the measure of the outer integration domains

- nested integrals cannot be reliably replaced by globally-adaptive schemes using

  a treap (tree-heap) and any adaptation scheme other than depth-first



## Algorithm



See the `notes` folder for a description of the IAI algorithm.

The implementation is based on [QuadGK.jl](https://github.com/JuliaMath/QuadGK.jl)



## Author and Copyright



IteratedIntegration.jl was written by [Lorenzo Van

Muñoz](https://web.mit.edu/lxvm/www/), and is free/open-source software under

the MIT license.



The algorithms in `IteratedIntegration.MeroQuadGK` and

`IteratedIntegration.ContQuadGK` were developed by [Alex

Barnett](https://github.com/ahbarnett/bz-integral) and are distributed

under the Apache 2.0 License



## Related packages

- [QuadGK.jl](https://github.com/JuliaMath/QuadGK.jl)

- [HCubature.jl](https://github.com/JuliaMath/HCubature.jl)

- [Integrals.jl](https://github.com/SciML/Integrals.jl)



[docs-stable-img]: https://img.shields.io/badge/docs-stable-blue.svg

[docs-stable-url]: https://lxvm.github.io/IteratedIntegration.jl/stable/



[docs-dev-img]: https://img.shields.io/badge/docs-dev-blue.svg

[docs-dev-url]: https://lxvm.github.io/IteratedIntegration.jl/dev/



[action-img]: https://github.com/lxvm/IteratedIntegration.jl/actions/workflows/CI.yml/badge.svg?branch=main

[action-url]: https://github.com/lxvm/IteratedIntegration.jl/actions/?query=workflow:CI



[pkgeval-img]: https://juliahub.com/docs/General/IteratedIntegration/stable/pkgeval.svg

[pkgeval-url]: https://juliahub.com/ui/Packages/General/IteratedIntegration



[codecov-img]: https://codecov.io/github/lxvm/IteratedIntegration.jl/branch/main/graph/badge.svg

[codecov-url]: https://app.codecov.io/github/lxvm/IteratedIntegration.jl



[aqua-img]: https://raw.githubusercontent.com/JuliaTesting/Aqua.jl/master/badge.svg

[aqua-url]: https://github.com/JuliaTesting/Aqua.jl



[ver-img]: https://juliahub.com/docs/IteratedIntegration/version.svg

[ver-url]: https://juliahub.com/ui/Packages/IteratedIntegration/UDEDl



[deps-img]: https://juliahub.com/docs/General/IteratedIntegration/stable/deps.svg

[deps-url]: https://juliahub.com/ui/Packages/General/IteratedIntegration?t=2