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Student Support Forum: '3-dimensional numerical integration' topicStudent Support Forum > General > Archives > "3-dimensional numerical integration"

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Michael Suchanecki
10/18/00 2:55pm

Hi,

I tried to perform a 3-dimensional numerical integration with Mathematica 4.0. The expression is of the form:

N[Integrate[Integrate[
If[w - j > 0, -3.989422804014327*^-13*Integrate[
E^(5.*^-9*(-Coth[1.*^-8*t]*(w - j)^2 - (w - j)^2 + t))*
Csch[1.*^-8*t]^(3/2), {t, 0, 4.}] - 1.9947114020071635*^-21*
(w - j)*Integrate[E^(5.*^-9*(-Coth[1.*^-8*t]*(w - j)^2 - (w - j)^2 +
t))*(-2*Coth[1.*^-8*t]*(w - j) - 2*(w - j))*
Csch[1.*^-8*t]^(3/2), {t, 0, 4.}], 0]*
If[j < 0, -3.989422804014327*^-13*Integrate[
E^(5.*^-9*(-Coth[1.*^-8*t]*j^2 + j^2 - t))*Csch[1.*^-8*t]^(3/2),
{t, 0, 4.}] - 1.9947114020071635*^-21*j*
Integrate[E^(5.*^-9*(-Coth[1.*^-8*t]*j^2 + j^2 - t))*
(2*j - 2*j*Coth[1.*^-8*t])*Csch[1.*^-8*t]^(3/2), {t, 0, 4.}], 0],
{j, -Infinity, Infinity}], {w, -Infinity, 1.2}]]

The evaluation ran for 96 (!) hours before I aborted it.

Is there a better algorithm than the standard method (Gauss-Kronrod) that is implemented in Mathematica? Is there a way to speed things up without losing much precision?


Thanks for any hint to solve the problem.

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