Re: help with double quadrature

[Carlo De Falco]

> On 11 Sep 2017, at 20:17, Clinton Winant <address@hidden> wrote:
> 
> I have to evaluate an integral over a triangular area:
> int_0^1 int_0^y [f(x,y)] dx,dy
> 
> Initially I though I could use dblquad, but is seems the integration limits 
> have to be numbers, not variables.  I have backed of to using quadgk to do 
> the inner integral, then summing over all y.  Does anyone know a better way?

Hi, 

The simplest approach is to use a (singular) affine trasformation that maps 
your triangle
into a square and a quadrature rule that does not place a quadrature node in 
the point of 
singularity, e.g. the method descibed in the section "Tensor product-type 
Gaussian quadrature 
- Simple but less efficient" in the document at this link:

  http://math2.uncc.edu/~shaodeng/TEACHING/math5172/Lectures/Lect_15.PDF

To implement this in Octave you can simply apply dblquad to the transformed 
integral that
you can see in the last formula on page 5 of the above reference.

But I think you should switch the backend of dblquad to something that does not 
place
quadrature nodes on the boundary of the domain, e.g. quadgk, rather than quadcc.

HTH,
c.