topic Re: My integration is not converging in Mathcad

My integration is not converging

SP_10712958 — Tue, 13 Jun 2023 06:51:33 GMT

I am trying to solve this problem for integration however i am facing not convergence issue. Please help me out.

Thanks

Re: My integration is not converging

terryhendicott — Tue, 13 Jun 2023 09:23:07 GMT

Hi,

There are unit inconsistencies in the equations.

Re: My integration is not converging

SP_10712958 — Tue, 13 Jun 2023 09:27:33 GMT

Thanks a lot, do you mean that dimensionality is not same, although both are energies in the numerator and denominator. So i think same or something is wrong.

Thanks

Re: My integration is not converging

terryhendicott — Tue, 13 Jun 2023 10:07:01 GMT

Hi,

T is not defined in the worksheet. Change the variable temp to T?

But it still does not converge.

Cheers Terry

Re: My integration is not converging

SP_10712958 — Tue, 13 Jun 2023 10:13:26 GMT

Thanks, Terry, as you said it does not still converge.

thanks

Re: My integration is not converging

terryhendicott — Tue, 13 Jun 2023 10:25:08 GMT

Hi,

A term gives a larger than capacity number depending on expected value of Ek.

Re: My integration is not converging

SP_10712958 — Tue, 13 Jun 2023 10:34:19 GMT

Thanks, Terry, do you mean we need to define Ek accordingly so that it would converge or what?

Thanks

Re: My integration is not converging

terryhendicott — Tue, 13 Jun 2023 11:39:28 GMT

Hi,

I mean that from the limits of integration for Ek of 0 to 1000 the term gives a number too large for Prime so integration fails

Re: My integration is not converging

Werner_E — Tue, 13 Jun 2023 13:38:55 GMT

Some Remarks:

Your definition of E.k seems to be wrong as the result possibly should be Energy

But as you never used it it does not affect the integral

For the integral to work you must also apply correct units for the integration limits!. E.g. Joule for the inner one and Hz for the outer one.

If you then set T:=temp (T was interpreted as unit Tesla as it was not defined) and a MUCH lower upper limit for E.k (I used 10^-19 J instead of your 1000) you get a result

I was even able to "push up" the upper limit to as much as 1.137*10^-19 J 😉

Terry had already shown that large values for E.k exceed Primes size limit for numbers (the usual IEEE limit).