# Catastrophic loss of precision

I am trying to solve a double integral in the range of 0 to Infinity (for both the integrals) and Mathematica is giving me the following error:

Catastrophic loss of precision in the global error estimate due to insufficient WorkingPrecision or divergent integral

Here is my code:

z = 2 + x + y;
s = 0.5;
m2 = 5325;
m1 = 5279;
mz = 10605.5;

NIntegrate[
1/z^3 (x + y + 2 x y) (1 + s^2/(2 m2^2 z)) Exp[-(m2^2 x + m1^2 y)/
s^2 + (mz^2 (x + y + 2 x y))/(2 s^2 z)], {x, 0, Infinity}, {y, 0,
Infinity}]


What does this error message mean, and how can I avoid it?

• The accumulation of error in the arithmetic of approximate Real numbers can sometimes get so great that a result loses all significance. To overcome, increase WorkingPrecision or post the actual problem and see if someone can help. Nov 18, 2014 at 3:36
• I am trying to solve for l = 2 + x + y; s = 0.5; m2 = 5325; m1 = 5279; mz = 10605.5; abc = NIntegrate[ 1/l^3 (x + y + 2 x y) (1 + s^2/(2 m2^2 l)) Exp[-(m2^2 x + m1^2 y)/ s^2 + (mz^2 (x + y + 2 x y))/(2 s^2 l)], {x, 0, Infinity}, {y, 0, Infinity}]
– NRS
Nov 18, 2014 at 3:53
• Please edit your question to include this. Nov 18, 2014 at 3:54
• I have edited and I am using Mathematica 10
– NRS
Nov 18, 2014 at 4:20
• Please change the letter l to something else, say L0. I can figure if I am looking at a 1 or l in your code, they look very much the same. Nov 18, 2014 at 4:51

I think the problem is that your integrand is just too large numerically to be handled correctly. Are you sure the expressions you are using are based on sound model or mathematics? The number they generate are so large. I can't imagine real physical problem will produce such values.

Trying just integrating over x by fixing y to see the problem. I went only to y=10

makeIntegrand[y_] := (
z = 2 + x + y;
s = 1/2;
m2 = 5325;
m1 = 5279;
mz = 106055/10;
b = x + y + 2 x y;
1/z^3 b (1 + s^2/(2 m2^2 z)) Exp[(-m2^2 x + m1^2 y)/s^2 + (mz^2  b)/(2 s^2 z)]
);

r = Table[{i, NIntegrate[makeIntegrand[i], {x, 0, Infinity}]}, {i, 0, 10, 1}];
r = Insert[r, {"y", "Integrate[...,{x,0,Infinity}]"}, 1];
Grid[r, Frame -> All]


• Thank you for responding. Actually I was trying to do mathematical analysis, but I think I am missing something. let me understand the problem again and then I will come back you. Thank you
– NRS
Nov 18, 2014 at 6:50
• the problem is solved, actually the value of factor "s" is 500 not 0.5.
– NRS
Nov 18, 2014 at 11:29