ABEL Transform Problem

[schneidrax]

[TheodoreM.Bones]

Letting x = 1.5, I cannot verify that g(1.5) = 0.325 in eiher natural or 10th power logs.

[ptc-1368288]

1. I have no red !
2. >The ordering of the variables under the square-root sign makes a difference to Mathcad. But why ? <<br>
Because of the meaning of the integrand is not the same. Try plotting both. In fact, G2 is asymptotic at x = 1.5 given y = 1.5, thus the complex value, by luck !!!

jmG

[TomGutman]

Seems to be a problem with your Mathcad version. I get the expected (by you) answer in both MC11 and MC14.

But the combination of numeric derivatives and numeric integrals make for a very slow calculation. Also note that you have an improper integral, with the integrand becoming infinite at one end point. Your version of Mathcad mmight just not support that, or might require explicitly choosing the singular endpoint option (by MC11 that and adaptive seem to be the same).
__________________
� � � � Tom Gutman

[TheodoreM.Bones]

Sometimes functions have two or more branches and perhaps only one is applicable to the transform.

[schneidrax]

On 9/4/2009 3:07:07 AM, Tom_Gutman wrote:
>Seems to be a problem with
>your Mathcad version. I get
>the expected (by you) answer
>in both MC11 and MC14.
>
I guess then MC2001i is the culprit.

>Also note that
>you have an improper integral,
>with the integrand becoming
>infinite at one end point.
>Your version of Mathcad mmight
>just not support that, or
>might require explicitly
>choosing the singular endpoint
>option (by MC11 that and
>adaptive seem to be the same).
>
Explicitly choosing the Singular Endpoint option doesn't help. And it's not required for the other three integrals, which seem content with the Adaptive option.

In my application worksheet, I had first chosen to use the problem transform pair and only stumbled onto the correct pair by chance. Like my old mentor advised, "Better to be lucky than smart."

Thank you all for looking at this problem. I guess we can chalk it up to a Mathcad 2001i bug.

[ptc-1368288]

>I guess we can chalk it up to a Mathcad 2001i bug.<<br> ______________________

You better hope some 2001i user opens your file, or even better from generosity: recreates the function. You deleted the error message. Did it say "Can't reach convergence" ? The red integral is "Adaptive". The one a left is "Singular end point".

jmG

[ptc-1368288]

... a supplementary detail:
My Mathcad 8 Pro used to fail for no reason, fail the "trunc(,,)". It reflected in nowhere to predict. But I have no recollection whether Beta testing or using 2001i that this version had this problem.

jmG

[schneidrax]

On 9/5/2009 5:50:17 PM, jmG wrote:

>You
>deleted the error message. Did
>it say "Can't reach
>convergence" ? The red
>integral is "Adaptive". The
>one a left is "Singular end
>point".

The three "correct" transforms perform properly with either "Adaptive" or "Singular Endpoint".

After claiming "Can't converge to a solution" the error message evaporated. Relaxing the tolerance to TOL = 0.1 led to convergence, but agreement was only to three places after the decimal.