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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
See the notes folder for a description of the IAI algorithm.
The implementation is based on QuadGK.jl
IteratedIntegration.jl was written by Lorenzo Van Muñoz, and is free/open-source software under the MIT license.