On 02/26/2010 12:20 PM, Anton Voropaev wrote:
> The integral of 1/sqrt(1-sin(x)^2*cos(y)^2) over [0,%pi/2]x[0,%pi/2]
> is known to be elliptic_kc(1/2)^2=3.437592909010188....
>
> The quad_qags function gives a quite accurate result: 3.437592909009772.
> While quad_ts does not: 2.64797046523282. See the code below.
> There is also a problem of using "x" as a variable name in the outer
> integral.
>
> How do I get more accurate quad_ts' output?
I'm guessing this is due to the fact that the tanh-sinh transformation
is designed for a 1D quadrature and you are employing it as iterated
integrals for 2D cubature. Perhaps the assumptions that make it accurate
are violated in this iterated scheme? I will be very interested to hear
if anyone has more info on what is going on here.