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Topic: integration help
Replies: 9   Last Post: Sep 15, 2006 8:55 AM

 Messages: [ Previous | Next ]
 regis lebrun Posts: 6 Registered: 9/14/06
Re: integration help
Posted: Sep 14, 2006 9:16 AM

John wrote:
> I've written an analytic routine to integrate the function
>
> f(x,y) = 1/sqrt((x-xo)^2+(y-yo)^2)
>

[...]
> Over the
> triangle 0<=x=<1, 0<=y<=x and (xo,yo)=(2/3,1/3), my analytic routine
> result is
>
> 2.4072299231640093
>
> Maxima returns (dblint_x=dblint_y=1000)
>
> 2.406741250203651
>

Maple 10 gives:
I =
-1/3*2^(1/2)*ln(-3+5^(1/2)*2^(1/2))-1/3*ln(-2+5^(1/2))+(-4/3-1/6*2^(1/2))*ln(2^(1/2)-1)+ln(2+5^(1/2))-2/3*arctanh(2/5*5^(1/2))-2/3*arctanh(1/2*2^(1/2))-1/6*2^(1/2)*ln(1+2^(1/2))
i.e.
I = 2.4072299231640097043

It seems that your routine is much more accurate than Maxima's one!

Regis LEBRUN

Date Subject Author
9/14/06 John
9/14/06 David W. Cantrell
9/14/06 John
9/14/06 regis lebrun
9/15/06 John
9/14/06 Paul Abbott
9/14/06 Julian V. Noble
9/15/06 John
9/15/06 Julian V. Noble
9/15/06 John