Iteration with an initial value

Question

Good morning community. I am trying to program to find a number α so that it meets a condition Psol=0.00 tonnef. In short, what I want is to enter an initial value α and until that condition Psol=0.00 tonnef is met, look for the value of α. Thank you for your attention, my version of Mathcad prime is V.9.0.
 
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Iteración con un valor inicial
 
Buen día comunidad. Estoy tratando de programar para buscar un número α para que cumpla una condición Psol=0.00 tonnef.  en resumen, lo que quiero es introducir un valor inicial α y hasta que no se cumpla esa condición Psol=0.00 tonnef busque el valor de α. Gracias por la atención prestada mi versión de Mathcad prime es V.9.0.

Werner_E · Accepted Answer

You define a variable alpha at the top and then carry out a series of calculations (mostly using the value of alpha or values derived from it) to calculate a value P.sol at the end.

Now you want to vary alpha in such a way as to obtain a specific value (zero) for P.sol.

It would be nice if you could turn the whole worksheet into a function with argument alpha.
Being able to do something like this is a very long-held wish, previously in Mathcad and now in Prime.
Unfortunately, this wish has not been fulfilled so far.

Therefore, you can only resort to more complicated and complex solutions.

One possibility is to rewrite all calculations that depend on alpha in some way as a function of alpha.

At the end you then have a function P.sol(alpha), the zero of which you can then search for either with the "root" function or with a solution block with "find".

There is a discrepancy concerning your desired value for M.sol.

You can solve for alpha to get that value for M.sol, but then P.sol is farther away from zero:

From the plot it looks like your calculations fail for some intermediate values (the red curve should not look dashed otherwise) - have not investigated any further, though.

Another approach could be to pack all the calculations into a single function P.sol(alpha). This is, given the worksheet already is provided for one run, a much greater effort, I suspect.

Worksheet for Prime 9 attached

MartinHanak · Answer

Hi,you cannot compare real number with fixed number (i.e. with zero). Define an interval of small values, i.e. < -epsilon, +epsilon > and compare Psol value with the boundaries of this interval. If the value of Psol is inside the interval, it will mean that it is "equal to zero".

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