0
$\begingroup$

I am trying to solve this expression with the function NIntegrate:

    NIntegrate[(2Subscript[b, 2])/(0.72*2\[Pi]^2*8.85418782*10^-12*3^2) (NIntegrate[( [Delta]*
    (3.482+\[Delta])EllipticE[-((4*0.1516*Subscript[b, 2])/((3.482+\[Delta])^2+
    (0.1516-Subscript[b, 2])^2))])/(((3.482+\[Delta])^2+(0.1516+Subscript[b, 2])^2)*
    Sqrt[(3.482+\[Delta])^2+(0.1516-Subscript[b, 2])^2]),{\[Delta],-0.36,0.36}]),{Subscript[b, 2],0,3}]

However, when I try to solve it gives me 3 of this error:

    NIntegrate::inumr: "The integrand (\[Delta]\(3.482 +\[Delta])\EllipticE[-((0.6064 
    Subscript[b, 2])/((3.482 +\[Delta])^2+(<<1>>)^2))])/(Sqrt[(3.482 +\[Delta])^2+
    (0.1516 -Subscript[b, 2])^2]\((3.482 +\[Delta])^2+(0.1516 +Subscript[b, 2])^2)) " has
    evaluated to non-numerical values for all sampling points in the
    region with boundaries {{-0.36,0.}}

By the way it gives the approximate value of my input but I wonder why it gives me these errors. Is it affecting the output? Thnaks.

$\endgroup$
  • $\begingroup$ You should comment on the answers you receive. If they are right, you should upvote/accept. If they are wrong you should explain why $\endgroup$ – Dr. belisarius Oct 26 '14 at 18:21
1
$\begingroup$

Your inner NIntegrate[] argument is of course non numeric because it depends on the outer NIntegrate[] variables. So,

f[d_, b_] := ((3.482 + d)^2 + (0.1516 - b)^2); 
NIntegrate[2 b ((d*(3.482 + d) EllipticE[-((4 0.1516 b)/f[d, b])])/(f[d, b] Sqrt[f[d, b]])), 
           {d, -0.36, 0.36}, {b, 0, 3}]

 (* -0.0103908 *)
$\endgroup$
1
$\begingroup$

You can use Quiet to silence the error warnings

NIntegrate[
  2 b2/(0.72*2 \[Pi]^2*8.85418782*10^-12*3^2) (NIntegrate[(d*(3.482 + 
          d) EllipticE[-(4*0.1516*
            b2/((3.482 + d)^2 + (0.1516 - b2)^2))])/(((3.482 + 
             d)^2 + (0.1516 + b2)^2)*
        Sqrt[(3.482 + d)^2 + (0.1516 - b2)^2]), {d, -0.36, 0.36}]), {b2, 0, 
   3}] // Quiet

-8.01331*10^6

or separate out the inner NIntegrate and define it for only numeric arguments

f[x_?NumericQ] := 
  NIntegrate[(d*(3.482 + 
        d) EllipticE[-(4*0.1516*
          x/((3.482 + d)^2 + (0.1516 - x)^2))])/(((3.482 + d)^2 + (0.1516 + 
           x)^2)*Sqrt[(3.482 + d)^2 + (0.1516 - x)^2]), {d, -0.36, 0.36}];

NIntegrate[2 b2/(0.72*2 \[Pi]^2*8.85418782*10^-12*3^2) f[b2], {b2, 0, 3}]

-8.01331*10^6

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.