Interative Solutions to Engineering/ETC. Problems

[Harold A Climer]

Many years ago when I was trying to be a double major
Physics/Engineering, I came across a class of problems that had to be
solved iteratively.
I remember having to do this type of problem in my Thermodynamics,
Heat and Mass Transfer,and Advanced Fluids classes.
I did some in of my upper level Physics classes too.
A few days ago one of our Junior Physics Majors came to me to ask me
if any General Type of Program to do this type of iteration is
available for an HP calculator.( She has an HP48GX and a HP50G)
It has been such a long time since I have done any of this myself; I
did not want to steer her in the wrong direction.
I do not come across this type of problem very often teaching 100 and
200 level Physics and Astronomy labs.
Harold A. Climer
Dept. Of Physics, Geology, and Astronomy
University of Tennessee at Chattanooga
309 Grote Hall
423-425-4546
Harold...@utc.edu

[J.Chen]

> Harold-Cli...@utc.edu

I believe there are a couple of programs in hpcalc.org that deals with
thermo iterations and heat transfer. But you have to be more specific
about what type of problems?

[PeterW]

As Chen already wrote, it is important to have an example of the
problems, which are under discussion.

Just to give a simple example:
the equation x = alpha * sin(x)
(where alpha is a constant) has at least
one solution x=0. Depending on the
value of alpha, it can have n solutions,
where n is any uneven number >= 1.

If you know, in which intervall you want to find a
solution, you can calculate the solution value easily
with a little iteration program or other numerical methods.
I think there are at least 3 different methods.

On the other hand it is really difficult to write a general
program to find all solutions automaticly, even for this very
simple specific problem.

[John H Meyers]

On Sat, 12 Apr 2008 14:57:47 -0500, PeterW wrote:

> If you know in which interval you want to find a [numeric]

> solution, you can calculate the solution value easily

> with a little iteration program or other numerical methods [ROOT ?]

> I think there are at least 3 different methods.
>
> On the other hand it is really difficult to write a general

> program to find all solutions automatically,

> even for this very simple specific problem.

"All roots" is in general impossible for a numeric solver
(e.g. 'SIN(1/X)=0.5' has an infinite number of solutions near X=0),
but it is easy to automate simple searching,
within a user-defined interval and specified "coarseness"
(size of fixed sub-intervals), e.g.:

ROOTS (UserRPL for any HP48G/49G/50G)
http://groups.google.com/group/comp.sys.hp48/msg/d9206945b20ed9aa
http://groups.google.com/group/comp.sys.hp48/msg/ce02637fba5af50f
http://www.hpcalc.org/search.php?query=allroots

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