Are there ways to compute cubatures of functions that include the Dirac delta function?

How are your functions represented? How would you be able to detect a delta function if you can only evaluate pointwise?

I have done this in the past by rewriting the target integral in a way that separates the dirac delta from the rest, analytically computing the integral w.r.t. the delta (it’s just the integrand’s value at the point) and then evaluating the leftover integral. I did this in a case where I had a proba…

Yeah, my bad. I know where the deltas are. Can I make cubatures step into these points somehow?

[image] homocomputeris: Can I make cubatures step into these points somehow? I don’t know of any integration packages that handle delta functions automatically, but as @tom-plaa wrote it should be easy to include the delta contributions separately from the rest of your integral. (A separate …

If you are interested in quadrature rules that can handle singularities, then you can use the Tanh-Sinh rule. Or do you want to use the dirac function properties in integrals?

[image] svretina: If you are interested in quadrature rules that can handle singularities, then you can use the Tanh-Sinh rule. That’s only for endpoint singularities.

[image] dlfivefifty: How are your functions represented? [image] svretina: Or do you want to use the dirac function properties in integrals? In general, I want to handle functions like where there can be several deltas in different variables, e.g. for a 3D case: f(x,y,z) = h(x)g(y)\d…

yes indeed, but then you just have to split your domain in subdomains and then sum the respective results from the subdomains.

[image] svretina: yes indeed, but then you just have to split your domain in subdomains and then sum the respective results from the subdomains. Still has nothing to do with delta functions, which can’t be represented as ordinary functions at all (because they aren’t — they are distributions)…

I agree, that’s why I asked if the OP needs something with regard to singularities or he/she wants something about Dirac functions solely

Quadratures and cubatures with Dirac deltas

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Quadratures and cubatures with Dirac deltas

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