Document about solving Volterra equation (second kind)

[jianzuo]

I have seen a discussion here about solving Volterra eq of the second kind:
https://discourse.julialang.org/t/using-approxfun-jl-to-solve-a-volterra-equation-of-the-second-kind/40203
But I failed to adapt it to my case: $B(y) = f(y) + \int_0^y K(x, y)*B(x) dx$. For example, say K(x, y) = 1 - exp(x+y)
f(x) = 3x^3.
How to compute B()?

Besides, I can not find any description of that Volterra() in ApproxFun.jl

[dlfivefifty]

@TSGut

[TSGut]

I believe this is the colleague I helped out on Julia discourse with their issue: https://discourse.julialang.org/t/how-to-solve-volterra-integral-equation-of-second-kind/94332

[TSGut]

Could also copy my implementation of the Volterra operator into MultivariateOPs.jl or ApproxFun directly after some tidying of the old code.

[jianzuo]

Thanks @TSGut . Yes, it is me. After exchanging with you there is some remaining issue for solving my case as you concluded in Julia discourse. I rechecked the method in ApproxFun, and got the solution for my problem. But I can not find the document about the Volterra() function. That is why I am asking.
And thanks again for your help and the library!

[TSGut]

I suspect that there isn't documentation for the Volterra function in ApproxFun yet. It may be possible to help you with questions you may have though.

What issue remains with my answer btw? I don't see anything about the posted equation that wouldn't be solved by the Sparse Volterra stuff.

[jianzuo]

Hi, the remaining issue is the problem of calling the pdf function as we have discussed in Julia discourse.
I quoted your reply here:
"Note that I have started an issue about the bug you had with the pdf example here. It may take some extra time but once that is fixed, it will work with the syntax you used as well."
Thanks!

[TSGut]

A helpful comment by @HadrienNU here JuliaApproximation/MultivariateOrthogonalPolynomials.jl#140 suggests that you can circumvent the problem by just defining the global variables you want to use as constants first. Can you give that a try and see if it helps with your issue?

[jianzuo]

Thank you very much @TSGut . I will check for the discussion you pointed out.