Integration methods...an error-proof method?

[Paul Dale]

(09-02-2017 09:42 PM)Matt Agajanian Wrote:  So, rather than this approach, what are some improved integration methods to avoid, aleviate, bypass, or resolve discontinuities in functions?

Avoiding the endpoints is straightforward, the rectangle method can do this by evaluating the rectangle mid-points.

I suspect this is impossible in general. A discontinuity between two evaluation points is going to be impossible to detect. Where both sides run to opposite signed infinities can be detected (e.g. tangent) but I'm not sure how helpful that is -- the area under each side could be infinite and then there is the question as to what infinity - infinity means?

Avoiding undefined evaluation points seems problematic -- it would be possible to shift the point on error and increase the resolution around the failure which would be a start. I'm sure it could be tricked up easily.


Pauli