HP-34C – Happy Anniversary!

[Willy R. Kunz]

(01-10-2019 09:44 PM)Dieter Wrote:  Yes, Solve and Integrate were powerful new functions on the 34C. They have been thoroughly discussed, and the manual uses many pages for explaining their use, interpreting the results and more.

Which leads to the question how all this is done by RPN34. Especially the 34C integration routine is quite sophisticated, and I wonder if this is also true for the emulator. As far as I know the algorithm has never been published, so the details are unknown. So: what are the methods that are implemented in RPN34? I assume they are not identical to the original algorithms, so the results can differ.

Dieter

According to the HP Journal Aug 1980, they used "a Romberg method", adding that "several refinements were found necessary". They go into some detail about how they produced nonuniformly spaced nodes in order to suppress resonance or aliasing. Finally, they (proudly) compare their solution with other integrators. Fascinating reading.

RPN-34 CE relies on Gauss-Legendre quadrature formulas of high-orders, along with high-precision abscissas and weights stored in tables. The display format does not affect the precision, so the uncertainty value the HP-34 returns in the Y register doesn't apply to RPN-34.