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Solving numerically a multiple integral

asked 2016-04-03 12:08:42 -0500

b0ira gravatar image

updated 2016-04-03 13:26:06 -0500

var("r1, r2, v1, v2")
tau(r1,r2,v1,v2)=((r1-r2)-0.8)/(v1-v2)
E(r1,r2,v1,v2)= exp(-tau(r1,r2,v1,v2)/3)*1.5/tau(r1,r2,v1,v2)^2
f(r1,r2,v1,v2)=exp(-(v1^2+v2^2)/2)*exp(-E(r1,r2,v1,v2)/2)

integral(integral(integral(integral(f(r1,r2,v1,v2),r1,0,10),r2,0,10),v1,-inf,inf),v2,-inf,inf)

RuntimeError: ECL says: In function GCD, the value of the second argument is 1.0 which is not of the expected type INTEGER

Could anyone help me please?

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Comments

Most likely related to http://trac.sagemath.org/ticket/14821 and keepfloat:true in Maxima

kcrisman gravatar imagekcrisman ( 2016-04-04 20:06:22 -0500 )edit

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answered 2016-07-28 07:09:48 -0500

mforets gravatar image

Have you tried scipy's nquad function? I think that in your problem special care has to be taken in the line $v_1=v_2$, but it can be handled with the opts parameter.

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Comments

Can you give specific syntax? (Maxima and GSL both have numerical integration that Sage syntax automatically supports, you could give all three!) Not sure how these support infinite bounds though.

kcrisman gravatar imagekcrisman ( 2016-07-28 07:40:22 -0500 )edit

The infinite bounds can be passed as [-np.inf, np.inf]. However I didn't manage to obtain an answer for OP's integral -- it takes ages to converge. Perhaps a Monte Carlo integration is more reliable in this case (see mcint).

mforets gravatar imagemforets ( 2016-07-29 07:26:15 -0500 )edit

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Asked: 2016-04-03 12:08:42 -0500

Seen: 162 times

Last updated: Apr 03 '16