This idea came to me while I was sitting in my Calc III class in sophmore year. I did some tests and it actually works pretty well. I haven’t seen anyone else write/do something like this before, so I think it might be novel. However, it is kinda niche and pretty trivial, so I don’t think it warrants a paper. So instead, I bless you guys, my faithful readers, to this neat result.
I also wrote a python package to facilitate the use of my result. Can be found here.
APPLICATIONS OF GREEN’S THEOREM FOR NUMERICAL QUADRATURE
Abstract:
Certain integrals of two variables over a planar region are divergent or may take significant wall time when computed numerically. This paper presents the usage of Green’s theorem to transform such integrals over a plane to a line integral over its boundary. This can reduce the order of a numerical integration from
Full report can be found here. Disclaimer: I wrote this in my 2nd year, so my writing and results are not as mature. I would’ve done a few things differently now.