Skip to main content
Mathematica

You are not logged in. Your edit will be placed in a queue until it is peer reviewed.

We welcome edits that make the post easier to understand and more valuable for readers. Because community members review edits, please try to make the post substantially better than how you found it, for example, by fixing grammar or adding additional resources and hyperlinks.

8
  • $\begingroup$ Is this a numerical integration without warning messages or were the warning messages suppressed? Would be nice to give a reference about improper integrals of this type. $\endgroup$ Commented Jan 18, 2022 at 21:19
  • $\begingroup$ @granularbastard I got no messages (V13.0). $\endgroup$ Commented Jan 18, 2022 at 21:20
  • $\begingroup$ The code fails if we double the values for both PrecisionGoal. Why is it so instable? $\endgroup$ Commented Jan 18, 2022 at 21:35
  • 1
    $\begingroup$ @granularbastard The integral is oscillatory, which invites numerical instability. The Levin rule tries to handle that in the $t$ integral. However, the maximum magnitude of the integrand (over $t$) is roughly proportional to $x$ as $x \rightarrow \infty$. As $x$ grows, numerical instability seems to return (that's my guess). Theoretically, it should be handled by increasing WorkingPrecision, but the computations take too long for me to verify it. $\endgroup$ Commented Jan 18, 2022 at 21:48
  • 5
    $\begingroup$ @user64494 (1) For a given $x$, the $dt$ integral converges, so strictly speaking the approximates the value, not the principal value. Do not let the numerical tricks fool you. They are done for speed and accuracy. (2) I already said the double integral diverges, and I don't understand why it needs repeating. (3) Your last action shows what a jerk you can be. $\endgroup$ Commented Jan 18, 2022 at 22:04